1. Tardigrade
  2. Question
  3. Mathematics
  4. If y=1+x+(x2/2 !)+(x3/3 !)+ ldots . .+(xn/n !) then (d y/d x)+(xn/n !)=

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $y=1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\ldots . .+\frac{x^{n}}{n !}$ then $\frac{d y}{d x}+\frac{x^{n}}{n !}=$

KCETKCET 2022

Solution:

$y=1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\cdots+\frac{x^{n}}{n !}$
$\frac{d y}{d x}=0+1+\frac{2 x}{2 \times 1 !}+\frac{3 x^{2}}{3 \times 2 !}+\cdots+\frac{x^{n-1}}{(n-1) !}$
$\frac{d y}{d x}+\frac{x^{n}}{n !}=1+\frac{2 x}{2 \times 1 !}+\frac{3 x^{2}}{3 \times 2 !}+\cdots+\frac{x^{n-1}}{(n-1) !}+\frac{x^{n}}{n !}= y$