Question

Find the sum to n terms of the series 

(i) 0.4 + 0.44 + 0.444 + ... to n terms

(ii) 3 + 33 + 333 + … to n terms

Answer 1

(i) 0.4 + 0.44 + 0.444 + … to n terms

(ii) S_n = 3 + 33 + 333 + … to n terms 

= 3[1 + 11 + 111 + … to n terms] 

= (3/9) [9 + 99 + 999 + … n terms] 

= (1/3) [(10 – 1) + (100 – 1) + (1000 – 1) + ... n terms] 

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