How would one begin to find a simple formula for

I have no idea where to begin

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- Jul 12th 2014, 05:33 PMReneGFinding closed-form expression for this sum
How would one begin to find a simple formula for

I have no idea where to begin - Jul 12th 2014, 09:51 PMProve ItRe: Finding closed-form expression for this sum
Why do you think there is a simple closed form expression for this sum?

- Jul 12th 2014, 11:14 PMReneGRe: Finding closed-form expression for this sum
The initial problem asks for a closed form expression, so I just assumed one existed.

- Jul 12th 2014, 11:53 PMProve ItRe: Finding closed-form expression for this sum
Well to start it might be worth writing out a cumulative sum and see if you can see a pattern...

- Jul 13th 2014, 08:51 AMtopsquarkRe: Finding closed-form expression for this sum
It does have a closed form. See here. You can always do an induction proof from here, but I have no clue how to derive it from scratch.

-Dan - Jul 13th 2014, 10:09 AMReneGRe: Finding closed-form expression for this sum
If I recall correctly, the following is a property of sums

On the RHS, the first sum obviously becomes

I found the 2nd sum by letting

Subtracting from yields

Plugging back in...

Is any of my reasoning is even correct? I have no idea how Wolfram Alpha got - Jul 13th 2014, 02:18 PMSorobanRe: Finding closed-form expression for this sum
(Rofl)Hello, ReneG!

Quote:

Find a closed-form expression for: .

The geometric series has: first term , common ratio and terms.

. . Its sum is: .

Hence, [3] becomes: .

. .