Question

Write the Maclaurin series for f(x) = x^7e^x5. (2 points) a) the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial b) the summation from n equals 0 to infinity of the quotient of x to the 12th power and the quantity n plus 5 factorial c) the summation from n equals 0 to infinity of the quotient of x to the quantity 5 times n plus 7 power and n factorial d) the product of x raised to the 5 times n power and the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial

Answer 1

Recall that

$e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}$

Then

$e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n}}{n!}$

and

$x^7e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n+7}}{n!}$