1/1*3+1/2*4+1/3*5+1/4*6+…+1/100*102=?
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![1/1*3+1/2*4+1/3*5+1/4*6+…+1/100*102=?](/uploads/image/z/8806219-43-9.jpg?t=1%2F1%2A3%2B1%2F2%2A4%2B1%2F3%2A5%2B1%2F4%2A6%2B%E2%80%A6%2B1%2F100%2A102%3D%3F)
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)