# Math Help - sigma notation and telescoping

1. ## sigma notation and telescoping

hi, i have a telescoping problem. i looked up the definition of "telescoping" and found as follows:
when each term of a sum cancels part of the next term, leaving only portions of the first and last terms at them end the sum is said to "telescope."

So, I have to evaluate the telescoping sum of:

the summation of (a to the base of k) - (a to the base of k-1) from k=1 to n

any tips would be appreciated thanks in advance!!

I'd love to help you, but I don't understand your language . . .

the summation of (a to the base of k) - (a to the base of k-1) from k=1 to n
. . . . . . . . . . . . . \______________/
. . . . . . . . . . . . .
What does that mean?

3. i'm sorry i wasn't sure how to type that. it is an "a" with a subscript/base of "k"

4. Simply expand it:
$\sum_{k=1}^n \left(a_k - a_{k-1}\right) = \left(a_1 - a_0\right) + \left(a_2 - a_1\right) + \left(a_3 - a_2\right) + \left(a_4 - a_3\right) +$ ${\color{white}.} \ \cdots + \left(a_{n-3} - a_{n-4}\right) + \left(a_{n-2} - a_{n-3}\right) + \left(a_{n-1} - a_{n-2}\right) + \left(a_{n} - a_{n-1}\right)$

Now look carefully. What terms cancel out and what terms are left?