Thursday, 30 November 2017

sequences and series - Summation of 1cdot3cdot5cdot7+3cdot5cdot7cdot9...


Find the sum of:




1357+3579+... till n terms.




My attempt:



I got the ith term to be (2i1)(2i+1)(2i+3)(2i+5)



Expansion gives: 16i4+64i3+56i2+16i15



Required: ni=1(16i4+64i3+56i2+16i15)




Using summation identities, I got:



16n(n+1)(2n+1)(3n2+3n1)30+64n2(n+1)24+56(n)(n+1)(2n+1)616n(n+1)215n



However, answer given is simply 110{(2n1)(2n+1)(2n+3)(2n+5)(2n+7)+1357}

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