Hello I have found a pretty complicated way of finding the sum to this series, and was wondering if anyone could help me to find a simpler way.
The sum of the series 1+2+3+4+....+n= n(n+1)/2
What is the sum of 2+6+20+....+n(n+1)=???
Hello I have found a pretty complicated way of finding the sum to this series, and was wondering if anyone could help me to find a simpler way.
The sum of the series 1+2+3+4+....+n= n(n+1)/2
What is the sum of 2+6+20+....+n(n+1)=???
If you are looking for sum of series:
$\displaystyle 2 + 6 + 12 + 20 + .... + n(n + 1) =? $
then its:
$\displaystyle 2 + 6 + 12 + 20 + .... + n(n + 1) = \frac{{n(n + 1)(n + 2)}}{3}$
You need to look for:
$\displaystyle 2(1 + 3 + 6 + 10 + ... + \frac{{n(n + 1)}}{2}) = 2(\frac{{n(n + 1)(n + 2)}}{6}) = \frac{{n(n + 1)(n + 2)}}{3}$
Look at this post:
http://www.mathhelpforum.com/math-he...1-2-3-4-a.html