Answer:
a) See the proof below.
b) 
Step-by-step explanation:
Part a
For this case we assume that we have the following series
and this series has a finite radius of convergence
and we assume that
for all n, this information is given by the problem.
We assume that the series converges at the point
since w eknwo that converges, and since converges we can conclude that:
For this case we need to show that converges also for 
So we need to proof that 
We can do some algebra and we can rewrite the following expression like this:
and we see that the last series is alternating.
Since we know that
converges then the sequence {
} must be positive and we need to have
And then by the alternating series test we can conclude that
also converges. And then we conclude that the power series
converges for
,and that complete the proof.
Part b
For this case we need to provide a series whose interval of convergence is exactly (-1,1]
And the best function for this 
Because the series
converges to
when
using the root test.
But by the properties of the natural log the series diverges at
because
and for
we know that converges since
is an alternating series that converges because the expression tends to 0.
Answer:
D.
Step-by-step explanation:
4/5 is greater because when you times it by 6 the numerator becomes 24 therefore it is greater
You have to multiply 750*100 and then divide 75,000 with 15, which gives you 5,000
Answer:
n=2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
11−8n=1−3n
11+−8n=1+−3n
−8n+11=−3n+1
Step 2: Add 3n to both sides.
−8n+11+3n=−3n+1+3n
−5n+11=1
Step 3: Subtract 11 from both sides.
−5n+11−11=1−11
−5n=−10
Step 4: Divide both sides by -5.
−5n
−5
=
−10
−5
n=2