What is the value of (1-13) (1-14) (1-15) (1-16) … (1-1n) - mathselab.com

What is the value of (1-1/3) (1-1/4) (1-1/5) (1-1/6) … (1-1/n)?

Question


What is the value of (1-1/3) (1-1/4) (1-1/5) (1-1/6) … (1-1/n)?


A. 2
B. n
C. 2/n
D. 2n


Answer: C. 2/n


Solution:


Given series is

(1-1/3) (1-1/4) (1-1/5) (1-1/6) … (1-1/n)

= 2/3 × 3/4 × 4/5 × 5/6 × ⋯ × (n−2)/(n−1) × (n−1) / n

=2/n


Hence, the series

(1-1/3) (1-1/4) (1-1/5) (1-1/6) … (1-1/n) = 2/n .






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