Question

Question #d27c8

Answer 1

a. `sum_(n=0)^oo 0.4^n =5/3`

b. `sum_(n=1)^oo(-0.1)^n/3=-1/33`

Explanation:

A geometric series is a series of the form `sum_n ar^n`. If `|r| < 1`, then we have `sum_(n=0)^ooar^n = a/(1-r)`
Both of the series in question are geometric series.

a. `sum_(n=0)^oo 0.4^n = 1/(1-0.4) = 5/3`

b. `sum_(n=1)^oo(-0.1)^n/3 = -1/3 + sum_(n=0)^oo(-0.1)^n/3`

`=-1/3+1/3sum_(n=0)^oo(-0.1)^n`

`=-1/3 + 1/3*1/(1-(-0.1))`

`=-1/3 + 1/3*10/11`

`=-1/33`