Question

Question B

i) Is there an important difference between “sum a_i, i=1 to infinity” and “sum a_n, n=1 to infinity” ? Explain.

ii) Is there an important difference between “sum a_i, i=1 to infinity” and “sum a_i, n=1 to infinity” ? Explain.

Answer #1

Question D:
i) Write out the first few terms of the series sum 9*0.1^n, n=1
to infinity
ii) What is the series equal to?
iii) What famous math “paradox” does this relate to?

State whether the given series converges or diverges, and
why.
#21 sum 1/n^5, n=1 to infinity
#22 sum 1/5^n, n=0 to infinity
#23 sum 6^n / 5^n, n=0 to infinity
#24 sum n^-4, n=1 to infinity
#25 sum sqrt(n), n=1 to infinity

Show that the map Q[X] → Q[X], sum^{n}{i=0}(a_nX^i) →
sum^{n}{i=0}(a_n(2X + 3)^i) , is an automorphism of Q[X],

Show that the series sum(an) from n=1 to infinity
where each an >= 0 converges if and only if for every
epsilon>0 there is an integer N such that | sum(ak )
from k=N to infinity | < epsilon

Determine if the series converges conditionally, converges
absolutely, or diverges.
/sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4)
/sum(n=1 to infinity) sin(4n)/4^n

suppose sigma n=1 to infinity of square root ((a_n)^2 +
(b_n)^2)) converges. Show that both sigma a_n and sigma b_n
converge absolutely.

if the sum from 1 to infinity of An converges for all n>1, does
that mean that An converges aswell and that An is always a finite
number?

Let Sum from n=1 to infinity (an) be a convergent
series with monotonically decreasing positive terms. Prove that
limn→∞ n(an) = 0.

find the Interval of convergence of
1. sum from {0}to{infinity} X ^ 2n / 3^n

*********I need question 6 answered which is from question 5
which is *********
Question 5 : Program Correctness I (1 point)
Use the loop invariant (I) to show that the code below correctly
computes
n P−1 k=0 2k
(this sum represents the sum of the first n even integers where
n ≥ 1).
Algorithm 1 evenSum(int n)
1: p = 2(n − 1)
2: i = n − 1
3: while i > 0 do
4: //(I) p = nP−1...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 15 minutes ago

asked 15 minutes ago

asked 19 minutes ago

asked 24 minutes ago

asked 24 minutes ago

asked 33 minutes ago

asked 40 minutes ago

asked 50 minutes ago

asked 50 minutes ago

asked 53 minutes ago

asked 54 minutes ago