Instructions

Write a program called

sinseries$.$py to compute the following sum:

$s=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}$dots$+\frac{x^{2n-1}}{(2n-1)!}(-1{)}^{(n-1)}$

Where $0x6\mathrm{.}28$ is a real number. The value of $n,$ which is to be determined by

the program, must be the smallest positive integer that satisfies the inequality

$\frac{x^{2n-1}}{(2n-1)!}d$ where $n1,d$ is a very small positive real number $($less than $1).$ The

values of $x$ and $d$ must be provided as inputs to the program. $n!$ is the factorial of

n$.$

The expected input$/$output behavior of the program is illustrated below for three

example inputs:

Enter a real number $x$ between $0$ and $6\mathrm{.}28,$ inclusive: $0\mathrm{.}52$

Enter a small positive real number :$0\mathrm{.}0001$

s : $0\mathrm{.}49688013020186006$

Enter a real number $x$ between $0$ and $6\mathrm{.}28,$ inclusive: $1\mathrm{.}57$

Enter a small positive real number : $0\mathrm{.}001$

s : $1\mathrm{.}0000032058668369$

Enter a real number $x$ between $0$ and $6\mathrm{.}28,$ inclusive: $3\mathrm{.}14$

Enter a small positive real number $d<mn\; id="EditorElement\_1356266">1</mn>$ : $0\mathrm{.}001$

s : $0\mathrm{.}0016136360330223744$

Hint: Add the terms of the sum one at a time. Stop when the last added term is

found to be less than or equal to $d$