Question

The sum of 100 terms of the series .9+.09+.009..........Will be

Answer 1

Answer:

1

Step-by-step explanation:

Sum = .9+.09+.009 + .......

The sum is a geometric progression (GP) with first term  a₁ = 0.9 and common ratio r = 0.1

The sum of the first  n   terms of a GP is given by:

Sₙ = a₁ (1 - rⁿ) / 1 - r

S₁₀₀ = 0.9 ( 1 - (0.1)¹⁰⁰)/ 1 - 0.1

       = 1 - (0.1)¹⁰⁰

        ~` 1 - 0

        ~`  1