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Algebra

1/2.4 + 1.3/ 2.4.6 + 1.3.5/ 2.4.6.8 + 1.3.5.7/ 2.4.6.8.10+....+ upto infinite terms is equal to?
Please tell me how do I simplify this question and get to the final answer which is 1/2.
Chapter name- Sequence and Series.
Thank you in advance.

Profile image of Anushka Khuspe
7 Years agoGrade
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1 Answer

Profile image of Aditya Gupta
7 Years ago
This is not a question of sequence and series, instead it belongs to binomial theorem with fractional indices.
First Use the expansion of (1-x)^(-1/2)
Then integrate (1-x)^(-1/2) from 0 to 1 
Now subtract one and multiply both sides by half to obtain the sum S as ½
 

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