Question

Find the sum of the series $1.2+{2.2}^2+{3.2}^2+......100{.2}^{100}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let, $s=1.2+{2.2}^2+{3.2}^2+......100{.2}^{100}$ --------(1)

To solve this type of AGP questions, we need to multiply the series with common ratio and then subtract the series after multiplication of common ratio with the original series.

Multiply by common ratio 2 in the equations 1
$2s={1.2}^2+{2.2}^3+......100{.2}^{101}$ ------(2)

Subtract equation 2 to equation 1
$-s=1.2+2^2+2^3+......{.2}^{100}-{100.2}^{101}$
$-s=\frac{2(2^{1}00-1)}{2-1}-{100.2}^{101}$
$-s=2^{101}-2-{100.2}^{101}=-{992}^{101}-2$
$s={99.2}^{101}-2$