Question

8 + 88 + 888 + ……. upto n terms =

• A. $\frac { 80 } { 81 } \left( 10 ^ { n } - 1 \right) - \frac { 8 n } { 9 }$
• B.
• C. $\frac { 80 } { 81 } \left( 10 ^ { n } - 1 \right) + \frac { 8 n } { 9 }$
• D. None of these

Answer 1

Answer: (A)

$\frac { 80 } { 81 } \left( 10 ^ { n } - 1 \right) - \frac { 8 n } { 9 }$

Answer 2

$\frac { 8 } { 9 }$[9 + 99 + 999 + ….. + t_n]

= $\frac { 8 } { 9 }$[(10 + 10² + …. + 10ⁿ) – n]

= $\frac { 8 } { 9 }$×

= $\frac { 80 } { 81 }$ [10ⁿ – 1] –