$\displaystyle \sum\limits_{k = 0}^{n} \frac{2(k + 1)}{(n + 1)(n + 2)}$ How do I solve this? My brain is failing me. Any advice would be great.
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Everything in the summand that does not contain a k can be factored out of the summand. What does that do for you?
$\displaystyle \frac{2}{(n + 1)(n + 2)}\sum\limits_{k = 0}^{n} (k + 1)$ So the summation becomes: $\displaystyle \frac{2}{(n + 1)(n + 2)} (1 + 2 + 3 + ... + n + (n + 1))$ My brain is still stuck. 40C/104F+ temps are killing me. >_<
maybe you remember this ... $\displaystyle 1+2+3+...+n = \dfrac{n(n+1)}{2}$
Also, $\displaystyle \displaystyle\sum_{k=1}^{n}1=n.$
wonder if the sum is full of typos or if the problem tries to bust you.
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