Question

Let $S=1.2+{2.2}^2+{3.2}^3+.....+{100.2}^{100}$. Then $S$ is equal to

• A. ${199.2}^{100}+2$
• B. ${198.2}^{199}+2$
• C. ${199.2}^{199}+2$
• D. None

Answer 1

The correct option is A ${199.2}^{100}+2$

$S=1.2+{2.2}^2+{3.2}^3+.........+{100.2}^{100}2S={1.2}^2+{2.2}^3+........+{100.2}^{101}-S=1.2+{1.2}^2+......+{100.2}^{100}-{1.2}^2-{1.2}^3...-{100.2}^{101}-S=1.2\left(\frac{2^{99}-1}{2-1}\right)-{100.2}^{101}S=-2^{100}+2+{100.2}^{101}={199.2}^{100}+2$