Question

Prove that the following sum is telescoping
SEE BELOW

Answer 1

\[\sum_{j=1}^{n}(a _{j}-a _{j-1})=a _{n}-a _{0}\]

Answer 2

I am not even sure how to start tackling this. It just says to "show that" those two things are equal where a0, a1..an is a sequence of real numbers.

Answer 3

@gabie1121 try to expand it :)
\[\Large (a_1-a_0)+(a_2-a_1)+(a_3-a_2)+(a_4-a_3)...\]

Answer 4

You'll see terms always cancel out, leaving you with two terms...
\[\Large (\cancel{a_1}-a_0)+(\cancel{a_2}-\cancel{a_1})+(\cancel{a_3}-\cancel{a_2})+(a_4-\cancel{a_3})...\]

Answer 5

ok awesome. thanks!