Find given that

but ans is

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- June 9th 2011, 08:36 PMPunchSummation
Find given that

but ans is - June 9th 2011, 09:26 PMSudharaka
You have taken, .

This is incorrect (substitute n=2 and the right hand side becomes undefined).

Much easier is to treat the summation without breaking it apart into two pieces.

You have to evaluate,

When r=1;

When r=2;

When r=3;

.

.

.

.

.

.

When r=n-1;

When r=n;

Adding all these together you will get the correct answer. - June 9th 2011, 09:52 PMPunch
- June 9th 2011, 09:55 PMPunch
wait, i think i see it, is this the method of differences?

- June 9th 2011, 09:59 PMTheCoffeeMachine
At this stage, you can just map the summands to each other, by, say, replacing r with r+1 for the first one:

Doing the above might seem bit hard/weird at first, but after few times it becomes so natural that you will never again want to write out terms and stuff! :] - June 9th 2011, 10:11 PMSudharaka
- June 9th 2011, 11:37 PMSoroban
Hello, Punch!

Quote:

Write out the terms . . .

. .

Inside the brackets, all terms cancel out except the first and last terms.

. .

Therefore: .