(666…..n times)2 + (888….n times) is equal to | MATH - nth TERM OF SPECIAL SERIES, SUM TO n TERMS AND INFINITE NUMBER OF TERMS | SolveeIt | Solveeit

Today, October 3

Question

(666…..n times)² + (888….n times) is equal to

A

$\frac { 4 } { 9 }$ (10ⁿ – 1)²

B

$\frac { 4 } { 9 }$ (10ⁿ – 1)

C

$\frac { 4 } { 9 }$ (10²ⁿ – 1)

D

$\frac { 4 } { 9 }$ (10²ⁿ – 1)²

Answer

$\frac { 4 } { 9 }$ (10²ⁿ – 1)

Explanation

Solution

(6666…n times)² + (888…n times)

̃ (6 + 60 + 600 + ….n times)²

+ (8 + 80 + 800+…n times)

̃ (10²ⁿ –1)