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I promised a friend that I could help her about math questions. Yet, I am stuck with a series question. I have written the open form of each term. And I have split the general term into multiples. I have tried many other versions of the general term. I couldn't... I need at least a pointer. Thanks.

$$a(n) = \frac2{n^2+2n}$$

What is the sum of first 9 terms of the series above?

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HINT

$$\dfrac2{n^2+2n} = \dfrac2{n(n+2)} = \dfrac1n - \dfrac1{n+2}$$ Now write the first few terms and see the cancellations happening...

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Do you mean:

$a_{n} = \frac{2}{n^2+2n}$ ?

If so, consider rexpressing $a_{n}$ using partial fractions.

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