Summation question

**Glitch** · February 2nd 2011, 03:25 AM

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

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

Any advice would be great.

**Ackbeet** · February 2nd 2011, 03:32 AM

Everything in the summand that does not contain a k can be factored out of the summand. What does that do for you?

**Glitch** · February 2nd 2011, 04:15 AM

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

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. >_<

**skeeter** · February 2nd 2011, 04:22 AM

maybe you remember this ...

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

**Ackbeet** · February 2nd 2011, 04:33 AM

Also,

$\displaystyle\sum_{k=1}^{n}1=n.$

**Krizalid** · February 2nd 2011, 06:26 AM

wonder if the sum is full of typos or if the problem tries to bust you.

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