可以幫我解出下列數學問題嗎?謝謝!!?

Sol
A=1-1/2+1/3-1/4+…+1/59-1/60
=(1+1/3+1/5+…+1/59)-(1/2+1/4+1/6+…+1/60)
=(1+1/3+1/5+…+1/59)+(1/2+1/4+1/6+…+1/60)-2*(1/2+1/4+1/6+…+1/60)
=(1+1/2+1/3+…+1/60)+-(1/1+1/2+1/3+…+1/30)
=(1/31+1/32+1/33+…+1/60)
91/[(k+1)(90－k)]
=[(k+1)+(90－k)/[(k+1)(90－k)]
=(k+1)/[(k+1)(90－k)]+(90－k)/[(k+1)(90－k)]
=1/(90－k)+1/(k+1)
=1/(k+1)+1/(90-k)
B=1/(31*60)+1/(32*59)+1/(33*58)+…+1/(45*46)
91B=91/(31*60)+91/(32*59)+91/(33*58)+…+91/(45*46)
=(1/31+1/60)+(1/32+1/59)+(1/33+1/58)+…+(1/45+1/46)
=1/31+1/32+1/33+…+1/60
So
A/B=91A/(91B)=91