巧算 1/2+1/3+2/3+1/4+2/43/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100=?
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巧算1/2+1/3+2/3+1/4+2/43/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100=?巧算1/2+1/3+2/3+1/4+2/43/4+1/5+2/
巧算 1/2+1/3+2/3+1/4+2/43/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100=?
巧算 1/2+1/3+2/3+1/4+2/43/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100=?
巧算 1/2+1/3+2/3+1/4+2/43/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100=?
运用公式:1/n+2/n+…+(n-1)/n=[1+2+3+…+(n-1)]/n=(n-1)/2 (n>=2,n为自然数)
1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+···+1/100+2/100+···+99/100
=1/2+2/2+3/2+…+99)/2
=(1+2+…+99)/2
=4950
1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+....+(1/100+2/100+....+99/100)=
1/2+1+3/2+2+5/2+.....50=2525
原式=(1/2)+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/100+2/100+...+99/100)
=1/2+(3*(3-1)/2/3)+(4*(4-1)/2/4)+...+(100*(100-1)/2/100)
=1/2+2/2+3/2+...+99/2
=(1+2+3+...+99)/2
=(100*99/2)/2
=2475
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