Question

GIVING MEDAL
find the sum of n terms of follwing
2/3 + 8/9 + 26/27 + 80/81+.... n terms

Answer 1

each term is 1 - (1/3)^n
so the sum could be expressed as
sum as i goes from 1 to n of 1 - the sum as i goes from 1 to n of (1/3)^i
which equals
n - ∑[1 to n] (1/3)^i

Answer 2

Can you explain further @Tonks

Answer 3

the sum of powers on thirds is
a(n) = (3^n-1)/2

In general, the sum of powers of 1/q is
a(n) = (q^n-1)/(q-1)