Find the sum to n terms of the given sequence is 8, 88, 888, ....

Solution:

The given sequence is 8, 88, 888, .... n terms .

S_n = 8 + 88 + 888 + .... n terms

= 8 [9 + 99 + 999 + .... terms]

= 8/9 [(10 - 1) + (100 - 1) + (1000 - 1) + .... n terms]

= 8/9 [(10 + 10² + 10³ + .... n terms) - (1 + 1 + 1 + .... n terms)]

= 8/9 [10 (10ⁿ - 1)/(10 - 1) - n]

= 8/9 [10 (10ⁿ - 1)/9 - n]

= 80/81 (10ⁿ - 1) - 8/9 n

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 18

Find the sum to n terms of the given sequence is 8, 88, 888,...

Summary:

The sum of the first n terms of the sequence 8, 88, 888, ... is 80/81 (10ⁿ - 1) - 8/9 n