The number 360 is increased by 25%. The result is then decreased by 50%. What is the final number?
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Notice that
That is, the <em>n</em>-th term (where <em>n</em> = -1, 0, 1, …, 9) in the sum on the left side has a partial fraction decomposition of
and in the sum, some adjacent terms will cancel and leave you with
Now solve for <em>x</em>, bearing in mind that we cannot have <em>x</em> = 0, -1, -2, …, -10 :
Combine the fractions on the left side:
Then we must have
so that either <em>x</em> = 2 or <em>x</em> = -11.