4分之1加28分之1加70分之1·····504分之1等于多少列个公式如何计算

504=2²×3²×74与28和70都不存在质因数“3”【如果】1/4+1/28+1/70+1/130+1/208+1/304+1/418+1/550那么原式=1/(1×4)+1/(4×7)+1/(7×10)+1/(10×13)+1/(13×16)+1/(16×19)+(1/(19×22)+1/(22×25)=1/3×[(1/1-1/4)+(1/4-1/7)+(1/7-1/10)+(1/10-1/13)+(1/13-1/16)+(1/16-1/19)+(1/19-1/22)+(1/22-1/25)]=1/3×(1-1/25)=1/3×24/25=8/25【如果】1/4+1/28+1/70+1/130+1/208+1/304那么原式=1/3×[(1/1-1/4)+(1/4-1/7)+(1/7-1/10)+(1/10-1/13)+(1/13-1/16)]=1/3×(1-1/16)=1/3×15/16=5/16