Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer. ∑[infinity]n=17n2−4n+3
12+2n6

It means also converges.

Step-by-step explanation:

The actual Series is::

The method we are going to use is comparison method:

According to comparison method, we have:

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

Now:

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

if p>1 then series converges. In oue case we have:

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means also converges.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)