_______________________n

Consider the summation SUM ( (1/i) - (1/(i+1)) )

____________________ i=1

Derive a formula for this sum in terms of n.

n

Hint: SUM ( A(i) - A(i+1) )

i=1

= (A(1)-A(2)) + (A(2)-A(3)) + ... + (A(n)-A(n+1)) (who cancels??)

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- Oct 31st 2009, 03:01 PMkashifzaidiSeries and Sequences..deriving the formula
_______________________n

Consider the summation SUM ( (1/i) - (1/(i+1)) )

____________________ i=1

Derive a formula for this sum in terms of n.

n

Hint: SUM ( A(i) - A(i+1) )

i=1

= (A(1)-A(2)) + (A(2)-A(3)) + ... + (A(n)-A(n+1)) (who cancels??) - Oct 31st 2009, 03:06 PMmr fantastic
- Nov 5th 2009, 05:29 AMkashifzaidi
Attachment 13692

I done the following according to my notes. My book says find the common thing and divide it by 2 on both sides. I cannot find any common. I dont know how do it futher..

Plz help me

This is a page from my book.

Attachment 13693 - Nov 5th 2009, 06:40 AMPlato
The answer is simply $\displaystyle \sum\limits_{i = 1}^n {\left( {\frac{1}

{i} - \frac{1}

{{i + 1}}} \right)} = 1 - \frac{1}

{{n + 1}}$

These are known as.**collapsing sums**

Here only the first and last terms remain after subtraction.