Question

How many terms of the series 1 + 2 + 4 + .... has the sum 511?

Answer 1

S_n = 511

a = 1

r = `2/1`

= 2 > 1

n = ?

`S_n = (a (r^n - 1))/(2 - 1) = 511`

= `(1 ((2)^2 - 1))/(2 - 1) = 511`

= 2ⁿ − 1 = 511

⇒ 2ⁿ = 512

⇒ 2⁹ = 512

n = 9