# Difficult Summation Problem Grade 12

1. Feb 17, 2012

### slapshotphil

Determine a formula for the sum of
$\sum$ iri-1
in terms of n and r.

I am stuck on this, i dont understand what to do with the "i" infront of the ri-1

i know that $\sum$ ri-1 = (1-rn ) /1-r

all sums are for an index of i=1 to n
I just don't know how to go any farther. Any help is greatly appreciated. Thanks!

Last edited: Feb 17, 2012
2. Feb 17, 2012

### Dick

You don't have any limits on your sum. You should. But here's a hint. The derivative of r^i with respect to r is i*r^(i-1).

3. Feb 17, 2012

### ehild

Use that dri/dr=iri-1.

ehild

4. Feb 17, 2012

### slapshotphil

how will finding the derivative of the sum help me find the formula for the sum?

5. Feb 17, 2012

### Dick

Define the sum first. If you don't have any limits on it, it doesn't mean anything.

6. Feb 17, 2012

### slapshotphil

the sum starts at (i=1) and ends at (n)

7. Feb 17, 2012

### ehild

What is the sum Ʃri from i=1 to i=n?

ehild

8. Feb 20, 2012

### slapshotphil

the sum of ri is....

1-rn
1-r

but for the derivative of that i got
(-nrn-1)(1-r) - (1-rn)(-1)
(1-r)2

which is not the correct answer...

any hints?

9. Feb 20, 2012

### Applejacks01

Your sum is incorrect. it should be [1-r^(n+1)]/[1-r] if its from i = 0 to n

So subtract the term where i = 0 to get the proper sum from 1 to n