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Help with Summation of Series! FP1

Hi,
I'm having a bit of trouble solving this problem in the summation of series topic on further pure 1.

The question is as follows:

Given that sum_(k=1)^n(a k^2+b k) = n^2(n+1) ,find the values of a and b

Can anyone help? As it won't let me type the summation sign... The equation on the left is a sigma with an upper limit of 'n' and a lower limit of 'k=1' with the equation being (ak^2+bk)

Thanks
Original post by apettah
Hi,
I'm having a bit of trouble solving this problem in the summation of series topic on further pure 1.

The question is as follows:

Given that sum_(k=1)^n(a k^2+b k) = n^2(n+1) ,find the values of a and b

Can anyone help? As it won't let me type the summation sign... The equation on the left is a sigma with an upper limit of 'n' and a lower limit of 'k=1' with the equation being (ak^2+bk)

Thanks


∑k=1nak2+bk=a∑k=1nk2+b∑k=1nk\displaystyle \sum_{k=1}^n ak^2 + bk = a \sum_{k=1}^n k^2 + b \sum_{k=1}^n k

Substitute the standard results from your formula book and factorise.

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