Wednesday, June 29, 2016

sequences and series - Find frac17+frac1cdot37cdot9+frac1cdot3cdot57cdot9cdot11+cdots upto 20 terms


Find S=17+1379+1357911+ upto 20 terms


I first multiplied and divided S with 135 S15=11357+1313579+1351357911+ Using the expansion of (2n)! 135(2n1)=(2n)!2nn! S=15[20r=1(2r)!2rr!(2(r+3))!2r+3(r+3)!] S=158[20r=1(2r)!r!(r+3)!(2r+6)!] S=1520r=11(2r+5)(2r+3)(2r+1)


How can I solve the above expression? Or is there an simpler/faster method?


Answer



Hint:


1(2r+5)(2r+3)(2r+1)=14(1(2r+3)(2r+1)1(2r+5)(2r+3))



No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...