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Q. The sum of the series:

1/2 + 1/6 + 1/12 + 1/20 ++…… infinite terms. ??

asked by Kanupriya Verma

[Wonder Boy]

We can see here that  the denominators are the product of consecutive integers.

so 1/2 + 1/6 + 1/12 + 1/20 +…… = 1/1.2 + 1/2.3 +1/3.4+ 1/4.5 + ….which of th form 1/n(n+1)

1/n(n+1) = [(n+1)-n]/n(n+1) =1/n-1/(n+1)

so  1/1.2 + 1/2.3 +1/3.4+ 1/4.5 + .. = 1- 1/2 +  1/2-1/3 + 1/3-1/4 + 1/4 – 1/5  +……. upto infinity = 1 Ans 

 

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