Question

Find the sum of n terms of the series 11 + 103 + 1005 + ....

• A. $\frac{10}{9}({10}^n-1)-1$
• B. $\frac{100}{99}({10}^n-1)+n^2$
• C. $\frac{10}{9}({10}^n-1)+n^2$
• D. $Noneofthese$

Answer 1

The correct option is D $Noneofthese$

Checking option (a), Put n = 1
$\frac{10}{9}({10}^n-1)-1=9$, so it is not correct.
Checking option (b), Put n = 1
$\frac{100}{99}({10}^n-1)+n^2$ is not equal to 11. so this is also not correct.
Checking option (c).Put n = 1
$\frac{10}{9}({10}^n-1)+n^2=11$.But just because this option satisfies n = 1, it should not be assumed to be correct
Let us check it for n = 2
Option (c) gives us 114. So, this is also not correct.
Normally, in these cases, checking the options till n = 2 guarantees the answer, but sometimes we need to check it till n = 3.