Question

$(666\dots \dots ndigits{)}^2+(888\dots \dots ndigits)$ is equal to

• A. $({10}^n-1)\times \frac{4}{9}$
• B. $({10}^{2n}-1)\times \frac{4}{9}$
• C. $\frac{4({10}^n-{10}^{n-1}-1)}{9}$
• D. $\frac{4({10}^n+1)}{9}$

Answer 1

The correct option is B $({10}^{2n}-1)\times \frac{4}{9}$

For 1 digit, the sum would be $6^2+8$; for 2 digits, the sum would be ${66}^2+88$ and so on. Checking the options gives us option (b) as the correct answer.