试证:1/n (n +1 )=1 /n -1 /n +1 (其中n是正整数)
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试证:1/n (n +1 )=1 /n -1 /n +1 (其中n是正整数)
试证:1/n (n +1 )=1 /n -1 /n +1 (其中n是正整数)
试证:1/n (n +1 )=1 /n -1 /n +1 (其中n是正整数)
证明:
∵1 /n -1 /n +1
=(n+1)/n(n+1)-n/n(n+1)
=[(n+1)-n]/n(n+1)
=1/n(n+1)
∴1/n (n +1 )=1 /n -1 /(n +1)
∵1 /n -1 /n +1
=(n+1)/n(n+1)-n/n(n+1)
=[(n+1)-n]/n(n+1)
=1/n(n+1)
∴1/n (n +1 )=1 /n -1 /(n +1)
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