Q. 45.0( 1 Vote )

Find the sum of the following finite series

(i) 1 + 0.1 + 0.01 + 0.001 + … + ( 0.1)9 (ii) 1 + 11 + 111 + … to 20 terms.

Answer :


(i) In the G.P.,

First term = 1


Common ratio = = 0.1


Sum of n terms =


Sum of 10 terms =


Sum of 10 terms =


(ii) Series = 1 + 11 + 111 + …..20 terms


Series = [9×(1 + 11 + 111 + …..)] ( Multiplying and dividing by 9)


Series = [9 + 99 + 999 + …..]


Series = [(10–1) + (100–1) + (1000–1) + …..]


Series = [10 + 100 + 1000 + ….. – (20×1)]


Series = [10 + 100 + 1000 + …..] –


We find the sum of 10 + 100 + 1000…..20terms as:


First term = 10


Common ratio = = 10


Sum of n terms =


Sum of 20 terms =


Sum of 20 terms =


Series = [] –


Series =


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