calculus with sum sign - Pollak habit formationWhy would I want to find the rate at which things were changing? Marginal cost, marginal revenue and profitReturn to sum of powers question.Changing the order summation and limit and proving a double-sequence identityHow to prove “square arrangement product” converges?What rules were used to find that $sin(2/x)-(2/x)cos(2/x)$ is the derivative of $y= xsin( 1/x)$?Take partial derivative of $sum_i=1^n (y_i - ae^x_i^2 -bx_i^3)^2$ with respect to aSolving for kinematics equations with calculus$textProve that if sum_i=1^m|a_i - x|=sum_i=1^n|b_i - x|$ Then $text m=n and a_j = b_j textfor0le jle n$Evaluate the Finite Sum with Binomial CoefficientSolving least squares with partial derivatives.

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Happy pi day, everyone!



calculus with sum sign - Pollak habit formation


Why would I want to find the rate at which things were changing? Marginal cost, marginal revenue and profitReturn to sum of powers question.Changing the order summation and limit and proving a double-sequence identityHow to prove “square arrangement product” converges?What rules were used to find that $sin(2/x)-(2/x)cos(2/x)$ is the derivative of $y= xsin( 1/x)$?Take partial derivative of $sum_i=1^n (y_i - ae^x_i^2 -bx_i^3)^2$ with respect to aSolving for kinematics equations with calculus$textProve that if sum_i=1^m|a_i - x|=sum_i=1^n|b_i - x|$ Then $text m=n and a_j = b_j textfor0le jle n$Evaluate the Finite Sum with Binomial CoefficientSolving least squares with partial derivatives.













0












$begingroup$


i have no clue what is happening regarding the sum sign in the following:



$$ m- fracp_ia_i(x_i-b_i) sum_j=1^n a_j+p_jb_j=0 $$



$$ with sum_j=1^n a_j=1:$$



$$ fracp_ia_i(x_i-b_i) +sum_j=1^n p_jb_j=m$$



Could someone make me a bit smarter, please?
How gets the sum sign in front of $pb$ and why does it change the sign? what are the steps in between or how is this rule called? And why is there still the sum sign when the sum of aj eqauls one?



Thanks in advance.



Momo










share|cite|improve this question









New contributor




Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 1




    $begingroup$
    You can separate the sum $sum (a_j + p_j b_j) = sum a_j + sum p_j b_j$. Now use the fact that $sum a_j = 1$. The change of sign is just due to the fact that a member of the equations has been moved to the other side of the equality.
    $endgroup$
    – TheSilverDoe
    Mar 11 at 12:04















0












$begingroup$


i have no clue what is happening regarding the sum sign in the following:



$$ m- fracp_ia_i(x_i-b_i) sum_j=1^n a_j+p_jb_j=0 $$



$$ with sum_j=1^n a_j=1:$$



$$ fracp_ia_i(x_i-b_i) +sum_j=1^n p_jb_j=m$$



Could someone make me a bit smarter, please?
How gets the sum sign in front of $pb$ and why does it change the sign? what are the steps in between or how is this rule called? And why is there still the sum sign when the sum of aj eqauls one?



Thanks in advance.



Momo










share|cite|improve this question









New contributor




Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 1




    $begingroup$
    You can separate the sum $sum (a_j + p_j b_j) = sum a_j + sum p_j b_j$. Now use the fact that $sum a_j = 1$. The change of sign is just due to the fact that a member of the equations has been moved to the other side of the equality.
    $endgroup$
    – TheSilverDoe
    Mar 11 at 12:04













0












0








0





$begingroup$


i have no clue what is happening regarding the sum sign in the following:



$$ m- fracp_ia_i(x_i-b_i) sum_j=1^n a_j+p_jb_j=0 $$



$$ with sum_j=1^n a_j=1:$$



$$ fracp_ia_i(x_i-b_i) +sum_j=1^n p_jb_j=m$$



Could someone make me a bit smarter, please?
How gets the sum sign in front of $pb$ and why does it change the sign? what are the steps in between or how is this rule called? And why is there still the sum sign when the sum of aj eqauls one?



Thanks in advance.



Momo










share|cite|improve this question









New contributor




Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




i have no clue what is happening regarding the sum sign in the following:



$$ m- fracp_ia_i(x_i-b_i) sum_j=1^n a_j+p_jb_j=0 $$



$$ with sum_j=1^n a_j=1:$$



$$ fracp_ia_i(x_i-b_i) +sum_j=1^n p_jb_j=m$$



Could someone make me a bit smarter, please?
How gets the sum sign in front of $pb$ and why does it change the sign? what are the steps in between or how is this rule called? And why is there still the sum sign when the sum of aj eqauls one?



Thanks in advance.



Momo







calculus






share|cite|improve this question









New contributor




Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited Mar 11 at 12:01









YuiTo Cheng

2,0592637




2,0592637






New contributor




Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked Mar 11 at 11:52









PetePete

1




1




New contributor




Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Pete is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







  • 1




    $begingroup$
    You can separate the sum $sum (a_j + p_j b_j) = sum a_j + sum p_j b_j$. Now use the fact that $sum a_j = 1$. The change of sign is just due to the fact that a member of the equations has been moved to the other side of the equality.
    $endgroup$
    – TheSilverDoe
    Mar 11 at 12:04












  • 1




    $begingroup$
    You can separate the sum $sum (a_j + p_j b_j) = sum a_j + sum p_j b_j$. Now use the fact that $sum a_j = 1$. The change of sign is just due to the fact that a member of the equations has been moved to the other side of the equality.
    $endgroup$
    – TheSilverDoe
    Mar 11 at 12:04







1




1




$begingroup$
You can separate the sum $sum (a_j + p_j b_j) = sum a_j + sum p_j b_j$. Now use the fact that $sum a_j = 1$. The change of sign is just due to the fact that a member of the equations has been moved to the other side of the equality.
$endgroup$
– TheSilverDoe
Mar 11 at 12:04




$begingroup$
You can separate the sum $sum (a_j + p_j b_j) = sum a_j + sum p_j b_j$. Now use the fact that $sum a_j = 1$. The change of sign is just due to the fact that a member of the equations has been moved to the other side of the equality.
$endgroup$
– TheSilverDoe
Mar 11 at 12:04










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