# Summation

• November 23rd 2009, 02:38 AM
Simplicity
Summation
My textbook states.

$-2\sum_{i=k-4}^{2}i=-(7-k)(k-2)$

But I got the summation to equal -2k+4. I don't see how the textbook got the LHS to equal to the RHS. Thanks in advance.
• November 23rd 2009, 03:41 AM
alexmahone
Quote:

Originally Posted by Simplicity
My textbook states.

$-2\sum_{i=k-4}^{2}i=-(7-k)(k-2)$

But I got the summation to equal -2k+4. I don't see how the textbook got the LHS to equal to the RHS. Thanks in advance.

$S_n=\frac{n}{2}(a+l)$

$n=2-(k-4)+1=7-k$

$a=k-4$

$l=2$

$-2\sum_{i=k-4}^{2}i=-2(\frac{7-k}{2})(k-4+2)$

$=-(7-k)(k-2)$