summation of series

• Dec 10th 2012, 11:01 AM
nitin1
summation of series
can you tell me how to calculate the sum of series : 1/(n*(n+1)*(n+2)) ?
• Dec 10th 2012, 11:09 AM
Plato
Re: summation of series
Quote:

Originally Posted by nitin1
can you tell me how to calculate the sum of series : 1/(n*(n+1)*(n+2)) ?

Is this the question, $\sum\limits_{n = 1}^\infty {\frac{1}{{n\left( {n + 1} \right)\left( {n + 1} \right)}}}~?$
• Dec 10th 2012, 11:12 AM
nitin1
Re: summation of series
no.. not till infinity... it's upto only n.. like from 1 to 3 or 1 to 4 or say 1 to n... and the question is summation of 1/(n*(n+1)*(n+2)) .. this is nth term of the series...
• Dec 10th 2012, 11:32 AM
Plato
Re: summation of series
Quote:

Originally Posted by nitin1
no.. not till infinity... it's upto only n.. like from 1 to 3 or 1 to 4 or say 1 to n... and the question is summation of 1/(n*(n+1)*(n+2)) .. this is nth term of the series...

Well note that $\frac{1}{n(n+1)(n+2)}=\frac{1}{2n}-\frac{1}{(n+1)}+\frac{1}{2(n+2)}$.

Write out several terms to see if some pattern is there.
• Dec 10th 2012, 11:45 AM
nitin1
Re: summation of series
i have got this result from someone...

S(n)= 1/4 - 1/(2*(n+2)*(n+1))...

it is correct even! can you tell me the steps taken so as to achieve this result ? please! thanks.