Thread: Summation of fraction

Hi Guys,

I need a little help with this summation problem.

Find in terms of n, the value of the following sum,



I looked around and found this is called a harmonic series and is divergent to infinity. But the required answer is,



Please Help! Thanks.

Breaking it up into two simpler fractions is exactly what you do. Note that the harmonic series is only divergent when you have an infinite number of terms. But this is a series of a fininte number of terms... This is actually a telescopic series.

Originally Posted by mathguy80

Hi Guys,

I need a little help with this summation problem.

Find in terms of n, the value of the following sum,



I looked around and found this is called a harmonic series and is divergent to infinity. But the required answer is,



Please Help! Thanks.

Is...

(1)

... so that is also [telescopic sum]...

(2)

Kind regards

This is very cool! I had studied a similar technique, when deriving,



I did not know that it's called a Telescopic series! Thanks @Prove It and @chisigma.

Originally Posted by mathguy80

This is very cool! I had studied a similar technique, when deriving,



I did not know that it's called a Telescopic series! Thanks @Prove It and @chisigma.

This is not a telescopic series. Here you would need to use induction or a proof-without-words, like this...