# Changing the Limits of a Summation

• January 3rd 2010, 09:46 PM
algorithm
Changing the Limits of a Summation
Hi,

http://i661.photobucket.com/albums/u...MCU/limits.jpg

The limits change from a variable in k to a variable in L. Then the summation sign is removed using some identity. I don't know how any of these two steps was carried out.

Thanks for any explanations.
• January 3rd 2010, 09:53 PM
mr fantastic
Quote:

Originally Posted by algorithm
Hi,

http://i661.photobucket.com/albums/u...MCU/limits.jpg

The limits change from a variable in k to a variable in L. Then the summation sign is removed using some identity. I don't know how any of these two steps was carried out.

Thanks for any explanations.

Substitute $l = k - 2 \Rightarrow k = l + 2$. $k = 2 \Rightarrow l = 0$ and $k = n \Rightarrow l = n - 2$.

To evaluate the new sum you're expected to recognise that you have a geometric series (the common ratio is r = 0.9) and you're expected to know the formula for the sum of a geometric series.