Question

Find the sum to n terms 8 + 88 + 888 + 8888 +.....

Answer 1

S_n = 8 + 88 + 888 + … upto n terms

 = 8(1 + 11 + 111 + … upto n terms)

 = 8/9(9 + 99 + 999 + … upto n terms)

 = 8/9 [(10 – 1) + (100 – 1) + (1000 – 1) +… upto n terms]

= 8/9 [(10 + 100 + 1000 + … upto n terms) – (1 + 1 + 1 +.... n times)]

But 10, 100, 1000, … n terms are in G.P. with 

a = 10, r = 100/10 = 10