I have the following series:
1+23⋅12+2⋅53⋅6⋅122+2⋅5⋅83⋅6⋅9⋅123+…
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+(1−13)1!(12)+(1−13)(2−13)2!(12)2+(1−13)(2−13)(3−13)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+424⋅3+526⋅3+627⋅5+…
=∞∑r=1r+22r+1r(r+1)
=∑(12rr−12r+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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