Question

Find the sum to n terms of the following;

1. 9+ 99 + 999 + ...... 

2. 4 + 44 + 444 + ......

Answer 1

1. S_n = 9 + 99 + 999 +………..

= 10 – 1 + 100 – 1 + 1000 – 1 +………..

= 10 + 100 + 1000 +…….-1-1-1-…….

= 10 + 10² + 10³ +………-n

\(\frac{10(10^n-1)}{10-1}-n\) = \(\frac{10(10^n-1)}{9}-n\)

2. S_n = 4 + 44 + 444 +………..

= 4(1 + 11 + 111 +……..)