Another Mathematics Test

Hello again,

Thanks for your replies in the previous test/question.

Here is another challenging question:

Prove that the Sum of the series F(r) = r^2 from 1 to n is equal to

1/6 (n + 1) (2n + 1)

Hint: There are two ways that i can suggest, either proof by induction or the method of differences used in series.

Here comes another one:

Solve the differential equations

dy/dt = -1 - 2t/y-t

dy/dt -(t/t^2 +3) y = 1

Um, is there a typo? Your series question doesn't work for n=2

1+4 = 5
(1/6)*(3)*(5) = 5/2

The last one wasn't challenging...

Why do you post these little math tests here? Judging from experience, most of the people who post here do not have a mathematical background...

It's more Calc II...I should crack open my classical electrodynamics book and give some real difficult problem (if you went to grad school for physics you'd know the book).

Um, is there a typo? Your series question doesn't work for n=2

Ya, it's hosed up, should be.

(n)(n + 1)(2n + 1) / 6

EDIT: Here is the answer I think, using induction. I'm no mathemetician, and seems to be off topic, so not tackling any diffeq today.

img14.imgspot.com...

TheMesh



[edit on 25-7-2005 by TheMesh]

Hello again,

Sorry that i made a mistake it should be n (n + 1) (2n + 1)/ 6

TN1

What's with the math problems in a Science & Tech forum? Am I missing something?