Math Is Fun Forum

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Product

The value of the product

where the nth factor is

, is

(A) 441 (B) 4041 (C) 4410 (D) 4001 (E) 4010

I found this question on one of those Math Competition papers. I don't think you are allowed to use a calculator, or it would probably be easy XD. So yeah... what's the fastest method, just multiplying everything one by one, or is there some scary (and possibly faster) product formula?

Last edited by Toast (2007-01-22 18:29:29)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Product

The answer is 400 plus 41.
Because when you multiply X by 1 point something, you just add the something fraction of X to X.  So for the first two terms, you have 4 and  add 5/4 of 4 to 4, which is 4 + 5, or 9.
See how the pattern is just the numbers in the fraction added together.

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igloo myrtilles fourmis

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Product

Hmm, that's quite interesting

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Product

John ... that is so well observed!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Product

That is a very nice method. I wouldn't have seen to do it that way.

A possibly less complicated method would be to write each bracket as a top-heavy fraction.

Then you get (4/1)*(9/4)*(16/9)*(25/16)*...*(441/400), and you can see that the top term of one fraction cancels with the bottom term of the next, and so you're left with just (441/1) = 441.

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Why did the vector cross the road?
It wanted to be normal.

RauLiTo

Member

From: Bahrain

Registered: 2006-01-11

Posts: 142

Re: Product

very very nice !!!

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