Prove that if $nge 2$ is an integer, then $1/n^2 < 1/(n-1) - 1/n$ [closed] Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Proving that $n|mimplies f_n|f_m$Proof by induction that the sum of terms is integerHow to prove that $n^5 - n$ is a multiple of $5$?$1!+2!+ldots+n!$ cannot be the square of a positive integerProve by strong induction that $2^n$ divides $p_n$ for all integers n ≥ 1Suppose $a in mathbbZ.$ Prove that $5 mid 2^na$ implies $5 mid a$ for any $n in mathbbN$Unsure of Where to Start - Prove by Mathematical InductionShow that $frac1n<ln n$, for all $n>1$ where n is a positive integerUse induction to prove that $3|(4^n − 1) $ for any integer $n geq 0$Prove that if $d$ is a common divisor of $a$ and $b$, then $gcd(a,b)/d = gcd(a/d,b/d)$.
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Prove that if $nge 2$ is an integer, then $1/n^2
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Proving that $n|mimplies f_n|f_m$Proof by induction that the sum of terms is integerHow to prove that $n^5 - n$ is a multiple of $5$?$1!+2!+ldots+n!$ cannot be the square of a positive integerProve by strong induction that $2^n$ divides $p_n$ for all integers n ≥ 1Suppose $a in mathbbZ.$ Prove that $5 mid 2^na$ implies $5 mid a$ for any $n in mathbbN$Unsure of Where to Start - Prove by Mathematical InductionShow that $frac1n<ln n$, for all $n>1$ where n is a positive integerUse induction to prove that $3|(4^n − 1) $ for any integer $n geq 0$Prove that if $d$ is a common divisor of $a$ and $b$, then $gcd(a,b)/d = gcd(a/d,b/d)$.
$begingroup$
Prove that if $nge 2$ is an integer, then $1/n^2 < 1/(n-1) - 1/n$
Unsure how to start this question! I've tried to prove by induction but I keep getting $n>1$?
induction integers cauchy-sequences
edited Mar 27 at 7:11
Thomas Klimpel
4,85111658
asked Mar 27 at 3:47
BiancaJaadeBiancaJaade
1
$endgroup$
closed as off-topic by Saad, John Douma, user21820, max_zorn, Strants Mar 28 at 20:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, John Douma, user21820, max_zorn, Strants
add a comment |
$begingroup$
Prove that if $nge 2$ is an integer, then $1/n^2 < 1/(n-1) - 1/n$
Unsure how to start this question! I've tried to prove by induction but I keep getting $n>1$?
induction integers cauchy-sequences
edited Mar 27 at 7:11
Thomas Klimpel
4,85111658
asked Mar 27 at 3:47
BiancaJaadeBiancaJaade
1
$endgroup$
closed as off-topic by Saad, John Douma, user21820, max_zorn, Strants Mar 28 at 20:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, John Douma, user21820, max_zorn, Strants
3
$begingroup$
Compute $frac1n-1-frac1n$.
$endgroup$
– Reveillark
Mar 27 at 3:51
add a comment |
$begingroup$
Prove that if $nge 2$ is an integer, then $1/n^2 < 1/(n-1) - 1/n$
Unsure how to start this question! I've tried to prove by induction but I keep getting $n>1$?
induction integers cauchy-sequences
edited Mar 27 at 7:11
Thomas Klimpel
4,85111658
asked Mar 27 at 3:47
BiancaJaadeBiancaJaade
1
$endgroup$
Prove that if $nge 2$ is an integer, then $1/n^2 < 1/(n-1) - 1/n$
Unsure how to start this question! I've tried to prove by induction but I keep getting $n>1$?
induction integers cauchy-sequences
induction integers cauchy-sequences
edited Mar 27 at 7:11
Thomas Klimpel
4,85111658
asked Mar 27 at 3:47
BiancaJaadeBiancaJaade
1
edited Mar 27 at 7:11
Thomas Klimpel
4,85111658
asked Mar 27 at 3:47
BiancaJaadeBiancaJaade
1
edited Mar 27 at 7:11
Thomas Klimpel
4,85111658
edited Mar 27 at 7:11
Thomas Klimpel
4,85111658
edited Mar 27 at 7:11
Thomas Klimpel
4,85111658
4,85111658
asked Mar 27 at 3:47
BiancaJaadeBiancaJaade
1
asked Mar 27 at 3:47
BiancaJaadeBiancaJaade
1
asked Mar 27 at 3:47
BiancaJaadeBiancaJaade
1
1
closed as off-topic by Saad, John Douma, user21820, max_zorn, Strants Mar 28 at 20:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, John Douma, user21820, max_zorn, Strants
closed as off-topic by Saad, John Douma, user21820, max_zorn, Strants Mar 28 at 20:31
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, John Douma, user21820, max_zorn, Strants
3
$begingroup$
Compute $frac1n-1-frac1n$.
$endgroup$
– Reveillark
Mar 27 at 3:51
add a comment |
3
$begingroup$
Compute $frac1n-1-frac1n$.
$endgroup$
– Reveillark
Mar 27 at 3:51
3
3
$begingroup$
Compute $frac1n-1-frac1n$.
$endgroup$
– Reveillark
Mar 27 at 3:51
$begingroup$
Compute $frac1n-1-frac1n$.
$endgroup$
– Reveillark
Mar 27 at 3:51
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
$$frac1n-1 -frac1n = frac1(n-1)n > frac1n^2$$
since $n-1<n$.
answered Mar 27 at 3:51
rolandcyprolandcyp
2,149422
$endgroup$
add a comment |
$begingroup$
By the addition rule for fractions, $frac1n-1 - frac1n = fracn - (n-1)n(n-1) = frac1n^2-n$. The result is immediate from there.
answered Mar 27 at 3:51
Ethan MacBroughEthan MacBrough
1,271617
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$$frac1n-1 -frac1n = frac1(n-1)n > frac1n^2$$
since $n-1<n$.
answered Mar 27 at 3:51
rolandcyprolandcyp
2,149422
$endgroup$
add a comment |
$begingroup$
$$frac1n-1 -frac1n = frac1(n-1)n > frac1n^2$$
since $n-1<n$.
answered Mar 27 at 3:51
rolandcyprolandcyp
2,149422
$endgroup$
add a comment |
$begingroup$
$$frac1n-1 -frac1n = frac1(n-1)n > frac1n^2$$
since $n-1<n$.
answered Mar 27 at 3:51
rolandcyprolandcyp
2,149422
$endgroup$
$$frac1n-1 -frac1n = frac1(n-1)n > frac1n^2$$
since $n-1<n$.
answered Mar 27 at 3:51
rolandcyprolandcyp
2,149422
answered Mar 27 at 3:51
rolandcyprolandcyp
2,149422
answered Mar 27 at 3:51
rolandcyprolandcyp
2,149422
answered Mar 27 at 3:51
rolandcyprolandcyp
2,149422
2,149422
add a comment |
add a comment |
$begingroup$
By the addition rule for fractions, $frac1n-1 - frac1n = fracn - (n-1)n(n-1) = frac1n^2-n$. The result is immediate from there.
answered Mar 27 at 3:51
Ethan MacBroughEthan MacBrough
1,271617
$endgroup$
add a comment |
$begingroup$
By the addition rule for fractions, $frac1n-1 - frac1n = fracn - (n-1)n(n-1) = frac1n^2-n$. The result is immediate from there.
answered Mar 27 at 3:51
Ethan MacBroughEthan MacBrough
1,271617
$endgroup$
add a comment |
$begingroup$
By the addition rule for fractions, $frac1n-1 - frac1n = fracn - (n-1)n(n-1) = frac1n^2-n$. The result is immediate from there.
answered Mar 27 at 3:51
Ethan MacBroughEthan MacBrough
1,271617
$endgroup$
By the addition rule for fractions, $frac1n-1 - frac1n = fracn - (n-1)n(n-1) = frac1n^2-n$. The result is immediate from there.
answered Mar 27 at 3:51
Ethan MacBroughEthan MacBrough
1,271617
answered Mar 27 at 3:51
Ethan MacBroughEthan MacBrough
1,271617
answered Mar 27 at 3:51
Ethan MacBroughEthan MacBrough
1,271617
answered Mar 27 at 3:51
Ethan MacBroughEthan MacBrough
1,271617
1,271617
add a comment |
add a comment |
3
$begingroup$
Compute $frac1n-1-frac1n$.
$endgroup$
– Reveillark
Mar 27 at 3:51