数列bn=1/(n(n+1)) 求bn的前N项的和,要有证明过程 Tn=n/(n+1)

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数列bn=1/(n(n+1)) 求bn的前N项的和,要有证明过程 Tn=n/(n+1)
数列bn=1/(n(n+1)) 求bn的前N项的和,要有证明过程 Tn=n/(n+1)

数列bn=1/(n(n+1)) 求bn的前N项的和,要有证明过程 Tn=n/(n+1)
bn=1/(n(n+1))=(1/n)-(1/(n+1))
Tn=(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/n)-(1/(n+1))
=1-(1/(n+1))
=n/(n+1)

bn=1/(n(n+1))=(1/n)-(1/(n+1))
Tn=(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/n)-(1/(n+1))
=1-(1/(n+1))
=n/(n+1)