Prove: The difference of the reciprocals of two successive integers equals the product of their reciprocals. 1 1

Question

Prove: The difference of the reciprocals
of two successive integers equals the
product of their reciprocals.
1
1
–
n
n + 1
[?]
n(n + 1)
[ ].[
n n+1

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Nho 5 years 2021-08-07T09:41:32+00:00 1 Answers 28 views 0

Answers ( )

  1. minhkhang
    0
    2021-08-07T09:42:36+00:00
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    Step-by-step explanation:

    let two successive integers n, n+1

    difference of the reciprocals:

    \frac{1}{n}-\frac{1}{n+1} \\=\frac{(n+1)-n}{(n)(n+1)}\\=\frac{1}{(n)(n+1)}\\=\frac{1}{(n)}\frac{1}{(n+1)}\\

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