Question

Find the sum to n terms 3 + 33 + 333 + 3333 + …..

Answer 1

S_n = 3 + 33 + 333 +….. upto n terms

= 3(1 + 11 + 111 +….. upto n terms)

= 3/9(9 + 99 + 999 + ….. upto n terms)

= 3/9[(10 – 1) + (100 – 1) + (1000 – 1) +… upto n terms]

= 3/9[(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