Question

The units’ digit of the sum 1 + 9 + 9² + ........ 9¹⁰⁰⁶ is 

(a) 2 

(b) 1 

(c) 9 

(d) 0

Answer 1

(d) 0

The units' digit of each term successively is 1, 9, 1, 9, ......... as the power of 9 is odd in the second term and even in the third term and so on. 

First term = 1 

The units' digit of first two term = 0 as 1 + 9 = 10, 

The units' digit of first three terms = 1 as 1 + 9 + 1 = 11 

The units' digit of first four terms = 0 as 1 + 9 + 1 + 9 = 20 

\(\implies\) Units' digit is 0 or 1 depending upon the number of terms whether even or odd.

\(\therefore\) Units' digit of the sum of 1006 terms, i.e., even number of terms = 0.