Question

Evaluate the geometric series. I need help please!!

Answer 1

4092

Explanation:

The n th term of a geometric series is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

4
`(2)^(n-1)` ← is the n th term

with a = 4 and r = 2

The sum to n terms of an arithmetic series is

`S_(n)` =
`(a(r^n-1))/(r-1)`, thus

`S_(10)` =
`(4(2^(10)-1) )/(2-1)`

= 4(1024 - 1) = 4 × 1023 = 4092