# general math problems

• Sep 26th 2006, 07:06 PM
yaszine
general math problems
hey hey,
i'm very new in here!!and i got a prob, actually two :
1. prove that any sum of more than 7 cents can be made up out of 3 cents and 5cents coins.
2.using mathematical induction, prove that for all n>1 the following inequality holds: 1/2squert + 1/3squert + .......+ 1/nsquert <1
• Sep 26th 2006, 07:24 PM
ThePerfectHacker
Quote:

Originally Posted by yaszine
hey hey,
i'm very new in here!!and i got a prob, actually two :
1. prove that any sum of more than 7 cents can be made up out of 3 cents and 5cents coins.

I am not going to post a proof of this, (I once did on this forum maybe I can find it).
But the result you can use is Sylvester's Coin Problem.
In this case,
(3)(5)-(3)-(5)=15-8=7
---
I do not understand the second question.
• Sep 27th 2006, 02:55 AM
topsquark
Quote:

Originally Posted by yaszine
Using mathematical induction, prove that for all n>1 the following inequality holds: 1/2squert + 1/3squert + .......+ 1/nsquert <1

The only thing I can think of here is that you mean:
1/sqrt(2) + 1/sqrt(3) +....+1/sqrt(n) < 1

However 1/sqrt(2) + 1/sqrt(3) = 1.28445705

-Dan
• Sep 27th 2006, 04:06 AM
ThePerfectHacker
Quote:

Originally Posted by topsquark
The only thing I can think of here is that you mean:
1/sqrt(2) + 1/sqrt(3) +....+1/sqrt(n) < 1

However 1/sqrt(2) + 1/sqrt(3) = 1.28445705

-Dan

Also, this sequence is the zeta function for x=1/2
Which by the integral test diverges, it much exceeds all numbers.
• Sep 27th 2006, 12:14 PM
yaszine
here's the problem
This is what i meant : 1 /(2 to the power 2) + 1/(3 to the power 2) + 1/(4 to the power 2) ………..+1/(nto the power two 2) < 1 !! i don't think it can ever be bigger than 1
• Sep 27th 2006, 12:42 PM
ThePerfectHacker
Quote:

Originally Posted by yaszine
This is what i meant : 1 /(2 to the power 2) + 1/(3 to the power 2) + 1/(4 to the power 2) ………..+1/(nto the power two 2) < 1 !! i don't think it can ever be bigger than 1

Here is the cowardly way of doing it.
The least upper bound for this series is,
pi^2/6-1<1
Thus, the partial sums must all be less than 1.
• Sep 27th 2006, 12:46 PM
yaszine
the thing is for my second question is to prove that the sum in the left is less or equal to 1 - 1/n !! but i don't know how !
for the first question, i couldn't see anyway i could solve it with that guy's coins' theory!!
anyways, thanks alot for help ! the hw is due tomorrow!! i'll scratch my head and see if i can solve it by midnight ! otherwise ...
thanks again!!
• Sep 27th 2006, 12:48 PM
ThePerfectHacker
Quote:

Originally Posted by yaszine
the thing is for my second question is to prove that the sum in the left is less or equal to 1 - 1/n !! but i don't know how !
for the first question, i couldn't see anyway i could solve it with that guy's coins' theory!!
anyways, thanks alot for help ! the hw is due tomorrow!! i'll scratch my head and see if i can solve it by midnight ! otherwise ...
thanks again!!

Tell your professor what I said. He will be proud of you, maybe give you extra credit.
• Sep 27th 2006, 12:49 PM
yaszine
:D i don't understand what u said, how did u come up with the answer? and what does pi have to do with this ?!! :D