Saturday, 13 April 2019

Evaluation of a series (possibly related to Binomial Theorem)

I have the following series:




1+2312+2536122+258369123+




I have to find the value of this series, and I have four options:
(A) 21/3 (B) 22/3 (C) 31/2 (D) 33/2




I can't seem to find a general term for this. I tried:



S=1+(113)1!(12)+(113)(213)2!(12)2+(113)(213)(313)3!(12)3+



But this doesn't seem to get me anywhere.



Any help?







This maybe a telescopic series, because there was a similar question we solved in class which ended up being telescopic:




323+4243+5263+6275+



=r=1r+22r+1r(r+1)



=(12rr12r+1(r+1))=12





P.S: This problem was included in my set of questions for Binomial Theorem, which is why I thought it might be related to it.

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