1/2+2*2/3+3*3/4+4*4/5+…+99*99/100等于多少?
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![1/2+2*2/3+3*3/4+4*4/5+…+99*99/100等于多少?](/uploads/image/z/47128-40-8.jpg?t=1%2F2%2B2%2A2%2F3%2B3%2A3%2F4%2B4%2A4%2F5%2B%E2%80%A6%2B99%2A99%2F100%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
1/2+2*2/3+3*3/4+4*4/5+…+99*99/100等于多少?
1/2+2*2/3+3*3/4+4*4/5+…+99*99/100等于多少?
1/2+2*2/3+3*3/4+4*4/5+…+99*99/100等于多少?
1/2+2*2/3+3*3/4+4*4/5+…+99*99/100
=(1-1/2)+2(1-1/3)+3(1-1/4)+4(1-1/5)+...+99(1-1/100)
=(1+2+3+4+...+99)-(1/2+2/3+3/4+4/5+...+99/100)
=[(1+99)×99÷2]-[(1-1/2)+(1-1/3)+(1-1/4)+..+(1-1/100)]
=4950-[100-(1+1/2+1/3+1/4+..+1/100)]
=4850+(1+1/2+1/3+1/4+..+1/100)
=4850+4.17737751763962
=4854.17737751763962
≈4854.177