cmi-entrance 2019 Q7

cmi-entrance · India · pgmath 4 marks Taylor series Identify a closed-form function from its Taylor series

The power series $$\sum_{n=1}^{\infty} \frac{n^2 x^n}{n!}$$ equals
(A) $x^2 e^x$;
(B) $x e^x$;
(C) $(x^2 + x) e^x$;
(D) $(x^2 - x) e^x$;

The power series
$$\sum_{n=1}^{\infty} \frac{n^2 x^n}{n!}$$
equals\\
(A) $x^2 e^x$;\\
(B) $x e^x$;\\
(C) $(x^2 + x) e^x$;\\
(D) $(x^2 - x) e^x$;