The Taylor series expansion of tan$1$ for $||<1$ is:

tan$1=3$

$3+5$

$5=(1)2+1$

$2+1$

$\backslash$infty

$=0$

Develop an algorithm that performs the following $($you can present it in the form of a

pseudo$-$code or a list of steps$)$:

The algorithm determines tan$1$ using the above equation, where the argument x is the

input, and the output argument y is the approximate value for tan$1$ obtained using

Taylor$$s series expansion. If $$ is the nth term of the series, then sum $$ of the first n

terms is $=1+.$ In each pass, calculate the estimated error E given by $=||.$

Stop adding terms when $<109,$ and report y$.$

Note: You are not asked to submit any code for this part. Submitting the algorithm is

sufficient.