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.
SAS hope this helps !!!!!!!
Answer:
there is no question below therefore, we can't answer it
Answer:
45
Step-by-step explanation:
c^2*b
We know that c is 3, and b is 5, so we can substitute them in
3^2*5
Solve the exponent first
9*5
Multiply
45
