Question

find the sum of 1/81 + 1/27 + 1/9.......+243​

Answer 1

Answer:

It's a geometric series, a convergent geometric series to be precise.

The given series,

1/3+1/9+1/27+1/81+1/243 ...∞

S (for infinite terms) = a₁/(1-r)

So, for the given series,

a₁ = 1/3

& r = aₙ/aₙ₋₁

=> r=(1/9) ÷(1/3)

=> r=1/3

Putting the values in the formula, we get

S=(1/3)/[1–(1/3)]

=> S=1/2=0.5

Ta-da, that's the required answer