Thread: Summing a series.

Sum the series

Sn = a + (a+d)r + (a+2d)r^2 + ... + [a+(n-1)d]r^(n-1)

n-1
Sum (a+nd)r^n
n=0

Presumably I need to split this up into a sum of ar^n and ndr^n

I have already summed ar^n, how would I go about summing ndr^n ?

Originally Posted by SunGod

Sum the series

Sn = a + (a+d)r + (a+2d)r^2 + ... + [a+(n-1)d]r^(n-1)

n-1
Sum (a+nd)r^n
n=0

Presumably I need to split this up into a sum of ar^n and ndr^n

I have already summed ar^n, how would I go about summing ndr^n ?

Split this up as follows:



and so on until


Then add all these sums, using the formula for geometric sums. There is also a way to do this with calculus.

Hey thanks for the solution, I've already handed in the work alas without the proof of that question, but at least now I know the logic behind working out a complicated summation like that (complicated on my level, anyway)

I've also read the other solution which requires calculus, thanks alot