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Is it possible to calculate prefix sums for sequnce defined as sum of two previous values
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Fibonacci series in 0-Even-Odd-Even-Odd-N series up to NRearranging a series of nonnegative termsFibonacci numeration systemNumber of possible sequences with at most 2 repetitions and entry $a_i in1,2,3,dots,i$Are the regular sequences of length $n$ one-to-one with the non-decreasing “complete” sequences of positive integers of length $n$?Calculate sum of small valuesVerifying that the $2n$-th term in a modified generalized Fibonacci sequence of order $n$ is the $n-1$-th Cullen numberWhat is the name of the “unique” numbers in Fibonacci-like integer sequences?Can I know the value of a sum of elements if I know what the sum of their squares is?Have I discovered a new significance to a previously discovered constant?
$begingroup$
Let's say we have sequence $S$ defined as: $S_1 = A, S_2 = B, S_i = S_i-1 + S_i-2, i > 2$.
We want to find the sum of the first $N$ elements of this sequence. Is there any easy and quick way to calculate this sum for any $A, B, N$.
What I did so far, if we define $F_i$ as the $i$-th fibonacci number, then we can write $S_i = F_i-2 * A + F_i-1 * B$. I already know that the sum of the first $N$ fibonacci numbers is $F_N+2 - 1$, however it turns out that this doesn't hold for any sequence $S$.
For example if $S = 1, 2, 3, 5, dots$ the sum of the first $2$ numbers is $3$, however $S_4 - 1 = 4$
sequences-and-series fibonacci-numbers
asked Mar 25 at 19:44
someone123123someone123123
464415
$endgroup$
add a comment |
$begingroup$
Let's say we have sequence $S$ defined as: $S_1 = A, S_2 = B, S_i = S_i-1 + S_i-2, i > 2$.
We want to find the sum of the first $N$ elements of this sequence. Is there any easy and quick way to calculate this sum for any $A, B, N$.
What I did so far, if we define $F_i$ as the $i$-th fibonacci number, then we can write $S_i = F_i-2 * A + F_i-1 * B$. I already know that the sum of the first $N$ fibonacci numbers is $F_N+2 - 1$, however it turns out that this doesn't hold for any sequence $S$.
For example if $S = 1, 2, 3, 5, dots$ the sum of the first $2$ numbers is $3$, however $S_4 - 1 = 4$
sequences-and-series fibonacci-numbers
asked Mar 25 at 19:44
someone123123someone123123
464415
$endgroup$
add a comment |
$begingroup$
Let's say we have sequence $S$ defined as: $S_1 = A, S_2 = B, S_i = S_i-1 + S_i-2, i > 2$.
We want to find the sum of the first $N$ elements of this sequence. Is there any easy and quick way to calculate this sum for any $A, B, N$.
What I did so far, if we define $F_i$ as the $i$-th fibonacci number, then we can write $S_i = F_i-2 * A + F_i-1 * B$. I already know that the sum of the first $N$ fibonacci numbers is $F_N+2 - 1$, however it turns out that this doesn't hold for any sequence $S$.
For example if $S = 1, 2, 3, 5, dots$ the sum of the first $2$ numbers is $3$, however $S_4 - 1 = 4$
sequences-and-series fibonacci-numbers
asked Mar 25 at 19:44
someone123123someone123123
464415
$endgroup$
Let's say we have sequence $S$ defined as: $S_1 = A, S_2 = B, S_i = S_i-1 + S_i-2, i > 2$.
We want to find the sum of the first $N$ elements of this sequence. Is there any easy and quick way to calculate this sum for any $A, B, N$.
What I did so far, if we define $F_i$ as the $i$-th fibonacci number, then we can write $S_i = F_i-2 * A + F_i-1 * B$. I already know that the sum of the first $N$ fibonacci numbers is $F_N+2 - 1$, however it turns out that this doesn't hold for any sequence $S$.
For example if $S = 1, 2, 3, 5, dots$ the sum of the first $2$ numbers is $3$, however $S_4 - 1 = 4$
sequences-and-series fibonacci-numbers
sequences-and-series fibonacci-numbers
asked Mar 25 at 19:44
someone123123someone123123
464415
asked Mar 25 at 19:44
someone123123someone123123
464415
asked Mar 25 at 19:44
someone123123someone123123
464415
asked Mar 25 at 19:44
someone123123someone123123
464415
asked Mar 25 at 19:44
someone123123someone123123
464415
464415
add a comment |
add a comment |
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