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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).

 Dec 13, 2022
 #1
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2n/n = 2

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

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

n > or = to 0.

1 - 0 = f(0)

1/2 = f(1)

1/3 = f(2)

1 - 3/(3 + 1) = 1/4 = f(3)

So you can see the pattern, and thus f(n) = 1/(n + 1)

 Dec 13, 2022

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