Recent content by danielbaker453

That's amazing! I was so focused on thinking of a test that would work that I didn't even pay attention to the very basics! Thanks for giving me this perspective.

Oh! I get it now. Thanks a lot!

I mean two series could be added in many different ways. For example, first term of one with the second of the other instead of adding term by term.

I did. But when I treated this absolute value series as a sum of two series, doesn't the order in which the terms of the two series are added matter?

But doesn't this proof of absolute convergence also assume that rearranging the terms has no effect of the convergence?

Okay... Now if I want to prove absolute convergence, I want to prove that the series ##\frac 1 {2^2}+\frac 1 {3^2}+\frac 1 { 2^3}+\frac 1 { 3^3}+...## is convergent. This can be viewed as the sum of two convergent geometric series and so it will be convergent as well proving that my series...

If I group the odd and even terms,I obtain ##\sum_{n=2}^\infty {(1/2^n)-(1/3^n)}## This is less than the geometric series ##\sum_{n=2}^\infty {(1/2^n)}## which is convergent. This makes my series convergent as well. However, if the original series were conditionally convergent, wouldn't...

Here is a plot of the magnitudes of a few terms. Although what you said is true( every even term is smaller than the preceeding odd term), every odd term after an even term is larger. How can I tell now whether the series is convergent or divergent?

These are my steps: I considered the even term as an=-1/(3^(0.5n+1)) which makes the odd term after it an+1=1/(2^(0.5n+2). The ratio rn=0.75*((1.5)^n) approaches infinity as n approaches infinity. This means that the series is divergent in this case. I plugged in n+1 for n to determine the odd...

Homework Statement Test the series for convergence or divergence ##1/2^2-1/3^2+1/2^3-1/3^3+1/2^4-1/3^4+...## Homework Equations rn=abs(an+1/an) The Attempt at a Solution With some effort I was able to figure out the 'n' th tern of the series an = \begin{cases} 2^{-(0.5n+1.5)} & \text{if } n...

Yes. I realize that my solution is wrong. This is not what I intended when I said I understand this. I meant to conserve momentum first and then energy. This is to show what I did wrong to anyone who is curious. Sorry for the confusion.

Thank you both! (BvU and TomHart) I finally understand this problem. Here is my work for anyone who is curious...

And that would be energy conservation for which the K.E. can be figured out using momentum conservation!

Also, here is a link to the solution I referred to

Yes! If it is dropped from a height the extension will be more as compared to when it is placed lightly.