# Summation question

• Feb 2nd 2011, 04:25 AM
Glitch
Summation question
$\sum\limits_{k = 0}^{n} \frac{2(k + 1)}{(n + 1)(n + 2)}$

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

• Feb 2nd 2011, 04:32 AM
Ackbeet
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, 05:15 AM
Glitch
$\frac{2}{(n + 1)(n + 2)}\sum\limits_{k = 0}^{n} (k + 1)$

So the summation becomes:

$\frac{2}{(n + 1)(n + 2)} (1 + 2 + 3 + ... + n + (n + 1))$

My brain is still stuck. 40C/104F+ temps are killing me. >_<
• Feb 2nd 2011, 05:22 AM
skeeter
maybe you remember this ...

$1+2+3+...+n = \dfrac{n(n+1)}{2}$
• Feb 2nd 2011, 05:33 AM
Ackbeet
Also,

$\displaystyle\sum_{k=1}^{n}1=n.$
• Feb 2nd 2011, 07:26 AM
Krizalid
wonder if the sum is full of typos or if the problem tries to bust you.