Why Is Maple Giving Incorrect Answers for Summations?

[stripes]

Homework Statement

Verify the following summations using Maple (see image).

Homework Equations

None

The Attempt at a Solution

For the first one, I enter

sum(k^3, k=1..n);

in Maple, and the result is

1/4*(n+1)^4-1/2*(n+1)^3+1/4*(n+1)^2,

which is definitely not the answer. Why is Maple giving me these weird and incorrect answers? The question is rather simple as I am just supposed to verify these summations using a computer, but for some reason, my computer seems to be complicating things.

 

[stripes]

Okay, so it seems if I type

factor(sum(k^3, k=1..n));

,

I get the correct answer. What gives?

 

[stripes]

Similarly,

sum(x^k, k=0..infinity);

1
- -----
x - 1

which = 1/(1-x).

But when I type

evalb(-1/(x-1) = 1/(1-x));

I obtain false. But they are equal! Am I completely missing something with Maple here?

 

[uart]

Hi stripes. Are you aware that there is usually more than one way to write any given mathematical expression, for example an expanded and a factorized form.

Look at a simple example.
$$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x(x+1)}$$
Writing it one way as opposed to the other makes it neither weird nor wrong.

 

[stripes]

Hi stripes. Are you aware that there is usually more than one way to write any given mathematical expression, for example an expanded and a factorized form.

Look at a simple example.
$$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x(x+1)}$$
Writing it one way as opposed to the other makes it neither weird nor wrong.

Oh, I understand that completely. I think most people on this forum do. What is puzzling me is that when I am given the expanded form, I don't immediately recognize it as being the correct answer because I am not quite a mathematician yet. So when I try to see if the expanded expression is equal to the factored expression, by using the evalb() operator in Maple, I get "false". I think one of my posts explained that. That's what's puzzling.

In other words, Maple is telling me 1/(1-x) =/= -1/(x-1), but they are, in fact, equal. This is my issue.

 

[uart]

Ok I see. I thought it was just the factorized versus expanded form of the expression that was confusing you.

I don't know why "evalb" returns false like that on expressions that seem obviously equivalent. Maybe if you post a question on that problem in the "Maths and Science Software" forum someone there may know.

 

[danielu13]

For the sum question, I have found that Maple tends to give expanded versions for some reason; to simplify that, just use the factor command. As far as the evalb thing, I've been messing around with Maple to try to figure it out, then looked on the website page for the evalb command, and there seems to be an issue of returning false for true equations when an equation is not simplified. This information can be found here.