1/1*3+1/2*4+1/3*5+1/4*6+…+1/100*102=?

1/1*3+1/2*4+1/3*5+1/4*6+…+1/100*102=?
1/1*3+1/2*4+1/3*5+1/4*6+…+1/100*102=?

1/1*3+1/2*4+1/3*5+1/4*6+…+1/100*102=?
1/1*3+1/2*4+1/3*5+1/4*6+…+1/100*102
=（1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/100-1/102）÷2
=（1+1/2-1/101-1/102）
=（3/2-203/10302）÷2
=15250/10302÷2
=7625/10302

=1/2 （1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.......1/99-1/101+1/100-1/102）
=1/2（1+1/2-1/101-1/102）
后面的都不是个事！！！

1/(n*(n+2)) = (1/n - 1/(n+2))/2
sigma(1/(n*(n+2))) [n=1->100] = 1/2*sigma(1/n-1/(n+2)) = ...

原式=1/2(1-1/3)+1/2(1/2-1/4)+......+1/2(1/100-1/102)
=1/2(1-1/3+1/2-1/4+1/3-1/5+......+1/98-1/100+1/99-1/101+1/100-1/102)
=1/2(1+1/2-1/101-1/102)
=7625/10302

1/1*3+1/2*4+1/3*5+1/4*6+…+1/100*102
=1/2*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/98-1/100+1/99-1/101+1/100-1/102)
=1/2*(1+1/2-1/101-1/102)
=25*(2/101+1/102)