Question

Suppose a series with only positive integers such that the sum of the terms is 1000. What can be the largest product of all the terms?

@ganeshie8
a little help here please

Answer 1

Suppose a series with only positive integers such that the sum of the terms is 1000. What can be the largest product of all the terms?

Answer 2

:O

Answer 3

My initial response was 2^500 but that is not correct

Answer 4

.

Answer 5

I think for rationals it might be the square root to the square root power.

Answer 6

So I would lean towards 32^8 * 31^24

Answer 7

nope it has to be bigger than 2^500

Answer 8

Hmm can't explain why but I found on a bit of research says split it into as many 3's as possible and 2's with the remainder.

Answer 9

so possibly 3^333 or 3^332*2^2

Answer 10

ah second case is larger of those.

Answer 11

@Evoker Your second choice is correct but how??

Answer 12

Ah well I did a bit of research, to be honest, the best explanation I can find uses Calculus, I'll try to find the article I found and post a link.

Answer 13

http://math.stackexchange.com/questions/125065/partitioning-a-natural-number-n-in-order-to-get-the-maximum-product-sequence-o

Answer 14

But it isn't a proof. In next part they are asking me to prove it

Answer 15

Ah the proof comes in the calculus bit, I believe

Answer 16

basically you need to split it into pieces as close to e as possible

Answer 17

3 being the closest number to e.

Answer 18

Tell me one thing. Why does the behaviour of a function remains same even if I apply logarithms on the whole function?
Like the value of x for which f'(x) is 0 is same even in g'(x) where g(x) is (ln(f(x))

Answer 19

Nevermind got it