Sunday, 19 February 2017

sequences and series - How to find the value of suminftyn=2frac3n5n(n21)



How can I calculate the sum of this series :



n=23n5n(n21)=?




I've tried to divide in factors 3n5n(n21) and obtained 5n(n1)+8(n1)(n+1). But when I try to expand the series I cannot make any simplifications. Can you please help me ? I've tried to divide in factors in different ways, but also got nothing. Thanks!


Answer



You can split it one step further as follows:
1n(n1)=1n11n,1(n1)(n+1)=12[1n11n+1]
Now both series telescope.


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