已知An=4n-2,若Bn=4/[An*A(n+1)],求Bn前n项和Tn

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已知An=4n-2,若Bn=4/[An*A(n+1)],求Bn前n项和Tn
已知An=4n-2,若Bn=4/[An*A(n+1)],求Bn前n项和Tn

已知An=4n-2,若Bn=4/[An*A(n+1)],求Bn前n项和Tn
Bn=4/[An*A(n+1)] = 4/[(4n-2)(4n+2)] = [1/(4n - 2)] - [1/(4n + 2)] ,
Tn = 1/2 - 1/6 + 1/6 - 1/10······ - [1/(4n + 2)]
= 1/2 - [1/(4n + 2)] = n/(2n + 1)

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