Question

The sum of 100 terms of the series .9+0.9+0.09 will be

Answer 1

Given: The series .9+0.9+0.09 .......

To find: The sum of 100 terms of the series.

Solution:

• Now we have given the series as 0.9+0.9+0.09 .......100th term

• We can write it as 9/10 + 9/10^2 + 9/10^3 ...........100th term

• Now we know that if a, b, c are in series, and if b/a = c/b, the the series is in GP.

• Similarly in this case this series is in GP. So:

• So :

                  9/10^2 / 9/10 = 9/10^3 / 9/10^2 = 1 / 10 = r

• And a = 9/10

• We know the summation formula:

                  S(n) = a(1 - r^n)/(1 - r)

                  S(n) = 9/10(1 - (1 / 10)^100) / 1 - 1/10

                  S(n) = 9/10(1 - (1 / 10)^100) / 9/10

                  S(n) = 1 - (1 / 10)^100

Answer:

             So the sum is 1 - (1 / 10)^100.