Multiplying fractions up to 2017 I recently came across this question, and I need some help with it (1−1/2)xx(1−1/3)xx(1−1/4)...(1−1/2016)xx(1−1/2017)= I have worked out that the pattern goes : 1/2xx2/3xx3/4... The last fraction will be 2016/2017, as with every fraction, the numerator and denominator increase by 1. However, how do I manage to multiply these?

Elena Simmons

Elena Simmons

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2022-08-26

Multiplying fractions up to 2017
I recently came across this question, and I need some help with it
( 1 1 / 2 ) × ( 1 1 / 3 ) × ( 1 1 / 4 ) . . . ( 1 1 / 2016 ) × ( 1 1 / 2017 ) =
I have worked out that the pattern goes :
1 2 × 2 3 × 3 4 ...
The last fraction will be 2016 2017 , as with every fraction, the numerator and denominator increase by 1. However, how do I manage to multiply these?

Answer & Explanation

Jaydon Villanueva

Jaydon Villanueva

Beginner2022-08-27Added 7 answers

The product telescopes: the terms cancel, like so:
1 2 × 2 3 × × 2016 2017 .
Thus the answer is 1 2017
Ronin Tran

Ronin Tran

Beginner2022-08-28Added 2 answers

n = 2 2017 ( 1 1 n ) = n = 2 2017 n 1 n = n = 2 2017 ( n 1 ) n = 2 2017 n = n = 1 2016 n n = 2 2017 n = 1 n = 2 2016 n 2017 n = 2 2016 n = 1 2017

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