Question

what is the sum of series 0.3+0.33+0.333+....n terms.

Answer 1

S = 0.3+0.33+0.333+.......n terms=3(0.1+0.11+0.111+.......n terms)=39(0.9+0.99+0.999+.... n terms)=13((1−0.1)+(1−0.01)+(1−0.001)+........... n terms)=13[n−(0.1+0.01+0.001+........n terms)]=13(n−0.1[1−(0.1)n]1−0.1)=13(n−0.1[1−(0.1)n]0.9)=13[9n−{1−(0.1)n}9]