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)](/uploads/image/z/15655324-4-4.jpg?t=%E6%95%B0%E5%88%97bn%3D1%2F%28n%28n%2B1%29%29+%E6%B1%82bn%E7%9A%84%E5%89%8DN%E9%A1%B9%E7%9A%84%E5%92%8C%2C%E8%A6%81%E6%9C%89%E8%AF%81%E6%98%8E%E8%BF%87%E7%A8%8B+Tn%3Dn%2F%28n%2B1%29)
n=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)
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)
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