Question

The sum of the series upto $n$ terms is.

• A. $\left( 10 ^ { n - 1 } - 9 n + 10 \right) / 81$
• B. $2 \left( 10 ^ { n + 1 } - 9 n - 10 \right) / 27$
• C. $2 \left( 10 ^ { n } - 9 n - 10 \right) / 27$
• D. None of these

Answer 1

Answer: (B)

$2 \left( 10 ^ { n + 1 } - 9 n - 10 \right) / 27$

Answer 2

Given series upto $n$ terms

upto $n$ terms

upto$n$terms$- n$

$= \frac { 2 } { 3 } \left( \frac { 10 \left( 10 ^ { n } - 1 \right) } { 10 - 1 } - n \right) = \frac { 1 } { 27 } \left[ 20 \left( 10 ^ { n } - 1 \right) - 18 n \right]$

$= \frac { 2 \left( 10 ^ { n + 1 } - 9 n - 10 \right) } { 27 }$.