1⼀4+1⼀12+1⼀24+1⼀40+……+1⼀19800 求详细解题过程!!!

解:原式1/4+1/12+1/24+1/40+……1/19800=1/4+1/12+1/24+1/40+……+1/19800
=(1/2)*[1/2+1/6+1/12+1/20+...+1/9900]
=(1/2)*[1/1*2+1/2*3+1/3*4+1/4*5+...+1/99*100]
=(1/2)*[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100]
=(1/2)*[1-1/100]
=(1/2)*(99/100)
=99/200
求采纳

解:原式1/4+1/12+1/24+1/40+……1/19800=1/4+1/12+1/24+1/40+……+1/19800
=(1/2)*[1/2+1/6+1/12+1/20+...+1/9900]
=(1/2)*[1/1*2+1/2*3+1/3*4+1/4*5+...+1/99*100]
=(1/2)*[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100]
=(1/2)*[1-1/100]
=(1/2)*(99/100)
=99/200

原式=(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)+……+(1/198-1/200)
=1/2-1/200
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