SOLUTION: Find the value of this product of 98 numbers (1 - 2/3) (1 - 2/4)(1 - 2/5).....(1 - 2/98) (1 - 2/99)(1 - 2/100) a 1/10 b 98/100 c 1/6 d 1/582120 e 1/4950

Click here to see ALL problems on Sequences-and-series

Question 292929: Find the value of this product of 98 numbers
(1 - 2/3) (1 - 2/4)(1 - 2/5).....(1 - 2/98) (1 - 2/99)(1 - 2/100)
a 1/10 b 98/100 c 1/6 d 1/582120 e 1/4950

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
(1 - 2/3) (1 - 2/4)(1 - 2/5)(1 - 2/6)(1 - 2/7)(1 - 2/8)(1 - 2/9).....(1 - 2/98) (1 - 2/99)(1 - 2/100) ... Start with the given product

(1/3)(1/2)(3/5)(2/3)(5/7)(3/4)(7/9)...(48/49)(97/99)(49/50) ... Subtract

Notice how the first denominator 3 cancels with the third numerator 3. Similarly, the second denominator 2 cancels with the 4th numerator 2. Also, the third denominator cancels with the 5th numerator 5. This pattern continues. So for the ith denominator (where 'i' is some positive integer), it cancels out with the i+2 numerator (ie go 2 terms down).

What this means that we're now left with:

(1)(1)(1)(1)(1)(1)(1)...(1)(1/99)(1/50)

Note: the 48 and 97 cancel out with denominators not shown (they are in previous terms).

Now simplify to get (1/99)(1/50) and multiply to get 1/4950

So the answer is E) 1/4950