$\displaystyle \sum\limits_{k = 0}^{n} \frac{2(k + 1)}{(n + 1)(n + 2)}$

How do I solve this? My brain is failing me. :(

Any advice would be great.

Printable View

- Feb 2nd 2011, 03:25 AMGlitchSummation question
$\displaystyle \sum\limits_{k = 0}^{n} \frac{2(k + 1)}{(n + 1)(n + 2)}$

How do I solve this? My brain is failing me. :(

Any advice would be great. - Feb 2nd 2011, 03:32 AMAckbeet
Everything in the summand that does not contain a k can be factored out of the summand. What does that do for you?

- Feb 2nd 2011, 04:15 AMGlitch
$\displaystyle \frac{2}{(n + 1)(n + 2)}\sum\limits_{k = 0}^{n} (k + 1)$

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. >_< - Feb 2nd 2011, 04:22 AMskeeter
maybe you remember this ...

$\displaystyle 1+2+3+...+n = \dfrac{n(n+1)}{2}$ - Feb 2nd 2011, 04:33 AMAckbeet
Also,

$\displaystyle \displaystyle\sum_{k=1}^{n}1=n.$ - Feb 2nd 2011, 06:26 AMKrizalid
wonder if the sum is full of typos or if the problem tries to bust you.