Difficult Summation Problem Grade 12

[slapshotphil]

Determine a formula for the sum of
\sum ir^i-1
in terms of n and r.

I am stuck on this, i don't understand what to do with the "i" infront of the r^i-1i know that \sum r^i-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!

 

[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).

 

[ehild]

Use that drⁱ/dr=ir^i-1.

ehild

 

[slapshotphil]

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

 

[Dick]

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

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

 

[slapshotphil]

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

 

[ehild]

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

What is the sum Ʃrⁱ from i=1 to i=n?


ehild

 

[slapshotphil]

the sum of rⁱ is...

1-rⁿ
1-r

but for the derivative of that i got
(-nr^n-1)(1-r) - (1-rⁿ)(-1)
(1-r)²

which is not the correct answer...

any hints?

 

[Applejacks01]

the sum of rⁱ is...

1-rⁿ
1-r

but for the derivative of that i got
(-nr^n-1)(1-r) - (1-rⁿ)(-1)
(1-r)²

which is not the correct answer...

any hints?

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