How can I calculate the sum of this series :
∞∑n=23n−5n(n2−1)=?
I've tried to divide in factors 3n−5n(n2−1) and obtained −5n(n−1)+8(n−1)(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(n−1)=1n−1−1n,1(n−1)(n+1)=12[1n−1−1n+1]
Now both series telescope.
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