Algebra

The given expression is $(666%20%5Cldots%20%5Ctext%7Bup%20to%20%7D%20n%20%5Ctext%7B%20digits%7D)%5E2%20%2B%20(888%20%5Cldots%20%5Ctext%7Bup%20to%20%7D%20n%20%5Ctext%7B%20digits%7D)$ .
We know that $666%20%5Cldots$ up to $n$ digits is represented as $%5Cfrac%7B2%7D%7B3%7D(10%5En%20-%201)$ and $888%20%5Cldots$ up to $n$ digits is represented as $%5Cfrac%7B8%7D%7B9%7D(10%5En%20-%201)$ . Now, square $666%20%5Cldots$ : $%5Cleft(%20%5Cfrac%7B2%7D%7B3%7D(10%5En%20-%201)%20%5Cright)%5E2%20%3D%20%5Cfrac%7B4%7D%7B9%7D(10%5E%7B2n%7D%20-%202%20%5Ctimes%2010%5En%20%2B%201).$ And for $888%20%5Cldots$ , we have: $%5Cfrac%7B8%7D%7B9%7D(10%5En%20-%201).$ Adding both, the final result is: $%5Cfrac%7B4%7D%7B9%7D(10%5E%7B2n%7D%20-%201).$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Algebra

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs