Yes consider the partial fraction expansion of .
Two of the fractions will telescope and you'll be done.
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You have a summation that starts at n=2.
Rewrite the summation of the second term by replacing n-1 by for instance k.
And rewrite the summation of the third term by replacing n+1 by m.
Afterward add or subtract whatever you need to, to make the summations start at 1.
Then you can combine them again.