1/2+2*2/3+3*3/4+4*4/5+…+99*99/100等于多少?

题目

1/2+2*2/3+3*3/4+4*4/5+…+99*99/100等于多少?

答案

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