It's possible to prove this by proving a stronger result by induction - that
Can you try to do that?
I need to prove that the product of 1/2 * 3/4 * 5/6 . . . 99/100 is less than 1/10. I understand that the product will continue to approach zero at a decreasing rate as the series progresses, but I need a mathematical explanation (of the most simple terms possible) as to why the product is less than 1/10.
Thank you very much, this problem has been driving me crazy. I'm in calculus 3, so this may be in the wrong section, but calculus 2 is the bound of my knowledge. If at all possible, lets keep it that simple. If not, blow me away anyways.
Induction is a technique used to prove statements like this one - Mathematical induction - Wikipedia, the free encyclopedia. Are you sure you haven't heard of it?
Assuming you proved the inequality I gave for every , if you put n = 50 you get the desired result.
If I set the term "1/2 * 3/4 * 5/6. . . 99/100" equal to A and create term B which equals "2/3 * 4/5 * 6/7. . . 98/99". This being the case, A < B. A * B = 1/100, and as 1/100 is 1/10 squared I have to prove that A^2 is less than 1/100. if A * B = 1/100 and A < B then A * A must be less than 1/100 and thus A < 1/10.
Does that work as a proof? I figured using a complimentary term might be easiest and as far as I can tell this works out. . .