求1*2,2*3,3*4,4*5,……,前99项的倒数之和.由此题你能总结出这类题的计算公式吗?
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![求1*2,2*3,3*4,4*5,……,前99项的倒数之和.由此题你能总结出这类题的计算公式吗?](/uploads/image/z/47132-44-2.jpg?t=%E6%B1%821%2A2%2C2%2A3%2C3%2A4%2C4%2A5%2C%E2%80%A6%E2%80%A6%2C%E5%89%8D99%E9%A1%B9%E7%9A%84%E5%80%92%E6%95%B0%E4%B9%8B%E5%92%8C.%E7%94%B1%E6%AD%A4%E9%A2%98%E4%BD%A0%E8%83%BD%E6%80%BB%E7%BB%93%E5%87%BA%E8%BF%99%E7%B1%BB%E9%A2%98%E7%9A%84%E8%AE%A1%E7%AE%97%E5%85%AC%E5%BC%8F%E5%90%97%3F)
求1*2,2*3,3*4,4*5,……,前99项的倒数之和.由此题你能总结出这类题的计算公式吗?
求1*2,2*3,3*4,4*5,……,前99项的倒数之和.由此题你能总结出这类题的计算公式吗?
求1*2,2*3,3*4,4*5,……,前99项的倒数之和.由此题你能总结出这类题的计算公式吗?
前99项和=(1-1/2)+(1/2-1/3)+...+(1/99-1/100)=1-1/2+1/2-1/3+...+1/99-1/100=1-1/100=99/100
总结公式:对于1*2,2*3,3*4,4*5,……,前n项的倒数之和(n为正整数)为n/(n+1)
1/1*2+1/2*3+1/3*4++1/4*5............+1/99*100
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5...........+1/99-1/100
=1/1-1/100
=99/100
总结
1/1*2+1/2*3+1/3*4++1/4*5............+1/n(n+1)
=n/(n+1)
1/(1*2)+1/(2*3)+1/(3*4)+...+1/(99*100)
=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=1-1/100
=99/100
公式:
1/(n(n+1))=1/n -1/(n+1)