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For a certain function f(n), the identity

(2n)/n - (2n)/(n + 1) = f(n) (2n)/n

for all nonnegative integers n.  Find f(n).

 Feb 10, 2023
 #1
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The f(n) = 1/(n+1) is the simplified form of the function.

(2n)/n - (2n)/(n + 1) = f(n) (2n)/n

Simplifying:

(2n)/n - (2n)/(n + 1) = 2f(n)

(2n)/2n - (2n)/2(n + 1) = 2f(n)/2

1 - n/(n+1) = f(n)

(n+1 - n)/(n+1) = f(n)

1/(n+1) = f(n)

 Feb 10, 2023

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