The question is: estimate the sum, from 2 to infinity, of 1 / (n^2 + 4) to within 0.1 of exact value.
I have the following: the integral from n to inf. of 1 / (x^2 + 4) is (pi/4 - 1/2 arctan(n/2)).
Next, in order to find the number of partial sums to use, set Sn + the integral from n+1 to...
The ratio test, I believe, is to use the limit as n goes to infinity of a(n+1) / a(n). So for detail:
cos (pi*(n+1))/5^(n+1) * 5^(n)/cos(pi*n).
I believe 5^n reduces with 5^(n+1) in the denominator, leaving 5 in the denominator, does it not?
Question says: \sum(cos(n*pi)/5^n) from 0 to infinity.
Proved that it converges: ratio test goes to abs(cos(pi*(n+1))/5cos(pi*n)) with some basic algebra. As n goes to infinity, this approaches -1/5 (absolute value giving 1/5) since cos(pi*(n+1))/cos(pi*n) is always -1, excepting the...
Hi,
Somebody asked me for some help with his calc II homework, and this was one of the questions:
"A hydra is a small freshwater animal and studies have shown that its probability of dying does not increase with the passage of time. The lack of influence of age on mortality rates for this...
Thank you very much. I'm certain my friend will appreciate this in the morning.
Funny how problems can be easier than they seem like this. The other day, I solved half of a Putnam question, then later failed to manage a basic geometry proof involving a circle. It's like sidestepping a pile of...
I thought that was for converting polar coordinates to rectangular.
Anyway, does that mean my solution for the second one is complete, and that the answer should just be r = 2 cos(θ)/sin2(θ)?
For the second one, I tried redoing the manipulation without substituting sqrt(x) for r. Should...
Homework Statement
I'm trying to help a friend with these two questions, but given that I haven't studied this material in over a decade, it's one of the topics I cannot recall at all.
Convert the following from rectangular to polar coordinates:
(a) x2 + y2 = x
(b) y2 = 2x...