Is there an easy way to calculate the following problem:
(1+1/2)(1+1/3)(1+1/4)............(1+1/102)(1+1/103)
2007-01-17 21:11:34 · 5 answers · asked by Amon R 2 in Education & Reference ➔ Homework Help
(1 + 1/2)(1 + 1/3)(1 + 1/4).......
(2/2+1/2)(3/3+1/3)(4/4+1/4)......
(3/2)(4/3)(5/4)...
Now, notice that the numerator of each term cancels with the denominator of the next. This eliminates all the numerators, and all but the first denominator, so you're left with
1/2
2007-01-17 21:17:43 · answer #1 · answered by Andrew 6 · 0⤊ 0⤋
Work out the brackets first. We get
3/2*4/3*5/4
Now we multiply the numerators 3*4*5 to get 60
Next, we multiply the denominators 2*3*4 to get 24
so we get 60/24. Remove the common multiple 12.
It comes to 5/2 i.e. 2 and1/2 (or that is 2.5 in decimals)
2007-01-18 05:48:25 · answer #2 · answered by young_friend 5 · 0⤊ 0⤋
(3/2)(4/3)(5/4)(...)= 3*4*5*.../2*3*4*...
= n!*1/2 / n! =1/2
2007-01-18 07:13:56 · answer #3 · answered by Salva 2 · 0⤊ 0⤋
u r asking me???? u know, i got 9/50 n last time i got 6/30!
2007-01-18 05:16:43 · answer #4 · answered by Anonymous · 0⤊ 0⤋
yes
what andrew says is right
2007-01-18 05:22:50 · answer #5 · answered by fun 5 · 0⤊ 0⤋