Question

How do you use summation notation to expression the sum `2-1/2+1/8-...+1/2048`?

Answer 1

`sum_(n=0)^6 [2*(-1/4)^n]`

Explanation:

This is a geometric sequence with a ratio of `(-1/4)`

The major problem is to determine the value of `n` for which `2 *(-1/4)^n` is equal to `1/2048`. This can be done by trial and error, although it helps to remember that `1024=2^10=4^5`