1. ## 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

2. 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.

3. 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

4. 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.

5. ## 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

6. 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.

7. 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!!

8. 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.

9. i don't understand what u said, how did u come up with the answer? and what does pi have to do with this ?!!