For every positive integer n, the function h(n) is defined

[gokul_nair1984]

I realised my error. Yes you just cannot take common factors in multiplication just as you do in addition or subtraction.

Thank You Ron

[RonPurewal]

I realised my error. Yes you just cannot take common factors in multiplication just as you do in addition or subtraction.

Thank You Ron

sure.

you should make a flash card of that particular operation (unsimplified version on the front, simplified version on the back), so that you can go over it and cement the knowledge in your head.

in fact, this is what you should do with almost all arithmetic and/or algebraic errors -- you should make flashcards of them. that way, after a while, you will have a deck of exactly the mistakes that you tend to make; that will be immensely valuable (and is something that you can't buy for any amount of money).

[steven.jacob.kooker]

@ Desert Rose:

The function h(n) is defined as 2*4*6*......*n

Therefore, h(100)=2*4*6*.....*100

Taking 2 common, h(100)= 2[1*2*3*.........*50]----(1)

whoa, no. there's no such thing as a "common factor" in multiplication!

if you're going to try to invent and/or verify rules like this one, you should check them first, with very easy numbers; if you've invented "rules" that are actually incorrect, you should be able to find this out fairly quickly by plugging in some numbers.

for instance,
(2x1) x (2x2) x (2x3) is 48.
2 x (1x2x3) is 12, which is not equal to 48.
so this "rule" doesn't work.

--

in this case you are just rearranging a whole bunch of numbers that are all multiplied together, so you need to keep all of the 2's:
(2x1) x (2x2) x (2x3) x ... x (2x50)
= (2x2x2x2x2x...x2) x (1x2x3x...x49x50)

so desert rose is correct.

So, ignoring all this stuff about 'factoring' multiples incorrectly, what's a good take away for this question (came up when I took the official prep tests from GMAC)? I feel as though the rule is: consecutive integers don't share factors other than one, so adding 1 to a factorial necessarily means the smallest prime of the new number is larger than the largest piece of the original factorial. Is this an accurate 'rule?'

[jlucero]

So, ignoring all this stuff about 'factoring' multiples incorrectly, what's a good take away for this question (came up when I took the official prep tests from GMAC)? I feel as though the rule is: consecutive integers don't share factors other than one, so adding 1 to a factorial necessarily means the smallest prime of the new number is larger than the largest piece of the original factorial. Is this an accurate 'rule?'

That's a great way to phrase the rule. In algebraic shorthand: (n! + 1) must have no prime factor between 1 and n.

For another OG example of this rule see:
does-the-integer-k-have-t4040.html