Question

Find the sum of 8+88+888+....up to n terms

Answer 1

Sum = 8+88+888+8888+…….(n terms).

= 8/9 * [ 9 + 99 + 999 + …….(n term)]

=8/9 * [ (10–1) + (100–1) + (1000–1) +…(nterm)]

=8/9 * [(10 + 10^2 +10^3 +…….+10^n) -n ]

=8/9 * [ 10*(10^n - 1)/9 - n]

=8/81 * [ 10^(n+1) - 9n -10 ].

Thanks.