Thanks. I'm new to this stuff and just now learning it otherwise I wouldn't be here asking for help. The question that was given to me seems misleading and suggests a possible solution, and I am trying to make sure that there hasn't been something I've been missing in my attempts, or am not yet...
As c is a constant I would say yes, this is a harmonic series as "2c" could be pulled out front. Then it would be divergent. I've already been down this road, and am trying to prove that it can converge with some value of c.
Well, set up as you have shown it
bk would be > ak for all values of c > 0 and the opposite if c < or equal to 0. Since we know 2/k+1 diverges, if bk < ak with c < or = 0, then ak would also diverge by the comparison test. Is this a correct assumption?
Given the establishment of an ak and bk...
The question states (verbatim): Determine all values of c such that the series converges. Then gives the below series.
. . . . .\displaystyle \sum_{k\, =\, 0}^{\infty}\, \dfrac{2}{ck\, +\, 1}
This one has been plaguing me for going on three days. It is the last problem in my current homework...
When I solved for C1 I got positive 3/2.
Using the value of C2 of -3/2, if C1 + C2 = 0, then C1 + -3/2 = 0, => C1 is +3/2
Reason this does not work is:
f(-1)=-2 does not equal 2(-1)^2 + (-1)^3 - 3/2
f(1) = 3 does not equal 2(1)^2 + (1)^3 - 3/2
C2-C1+C2+C1 = -3 + 0
C2 + C2 = -3
2C2 = -3
C2 = -3/2
This does not seem correct... and this value of C2 will not give me the correct function values as shown in the problem. I think I misunderstand what you're asking me to do. I apologize, and thank you very much for the help!
C2 + C1 = 0
+C2 - C1 = -3
I apologize, I'm hoping I am understanding what you are asking me to do... add the resulting equations together? Or the results? 0 + -3 = -3?
Whoops, sorry - thank you for spotting that. :) I input the wrong value in on the other side of the equation. This is what I got for evaluating f(-1) (correctly this time)
f(-1) = 2(-1)^2 + (-1)^3 + C1(-1) + C2
-2 = 2 - 1 - C1 + C2
-2 = 1 - C1 + C2
-3 = C2 - C1
Well.. that's assuming C1 is a...
Hi Stapel, thank you for the response. I didn't eliminate the other variable correctly past Step 3, part a... beyond that is where it fell apart. When I did the problem originally I incorrectly assumed it was giving me two different function values that could be used to solve for the C in the...
Hi all,
This is my first time posting in here, so I'm hoping I can find some help with this one problem that has been giving me trouble. I am currently wrapping up a Calculus I class for college, and have completed all required assignments (even the ones that are due two weeks from now), yet I...
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