I need to find the product: (1-1/2)(1-1/3)(1-1/4)(1-1/5)......(1-1/499)(1-1/500) = NOTICE: The list goes from (1-1/2) all the way to (1 - 1/500). How do I solve this question? How do I find the product?
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Originally Posted by magentarita I need to find the product: (1-1/2)(1-1/3)(1-1/4)(1-1/5)......(1-1/499)(1-1/500) = NOTICE: The list goes from (1-1/2) all the way to (1 - 1/500). How do I solve this question? How do I find the product? 1-1/2 = 1/2 1-1/3 = 2/3 1-1/4 = 3/4 1-1/5 =4/5 . . . 1-(1/499) = 498/499 1-(1/500) = 499/500 Multiply all these terms cancel common terms in numerator and denominator. Ans = 1/500
Originally Posted by ADARSH 1-1/2 = 1/2 1-1/3 = 2/3 1-1/4 = 3/4 1-1/5 =4/5 . . . 1-(1/499) = 498/499 1-(1/500) = 499/500 Multiply all these terms cancel common terms in numerator and denominator. Ans = 1/500 Indeed you do. For n terms this will be
Originally Posted by ADARSH 1-1/2 = 1/2 1-1/3 = 2/3 1-1/4 = 3/4 1-1/5 =4/5 . . . 1-(1/499) = 498/499 1-(1/500) = 499/500 Multiply all these terms cancel common terms in numerator and denominator. Ans = 1/500 How do I use the formula (1 - n)!/n! = 1/n to find the same answer?
Originally Posted by e^(i*pi) Indeed you do. For n terms this will be How do I use the formula (1 - n)!/n! = 1/n to find the same answer?
Originally Posted by magentarita How do I use the formula (1 - n)!/n! = 1/n to find the same answer? Your formula is not correct Remember that (n-1)! is not equal to (1-n)!
Originally Posted by ADARSH Your formula is not correct Remember that (n-1)! is not equal to (1-n)! I see what I did wrong.
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