逆向运用不等式1/a-1/b=b-a/ab,如1/12=4-3/3×4=1/3-1/4,根据上述等式计算1+1/2+1/6+1/12+…+1/n(n+1)n为整数
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![逆向运用不等式1/a-1/b=b-a/ab,如1/12=4-3/3×4=1/3-1/4,根据上述等式计算1+1/2+1/6+1/12+…+1/n(n+1)n为整数](/uploads/image/z/2811864-48-4.jpg?t=%E9%80%86%E5%90%91%E8%BF%90%E7%94%A8%E4%B8%8D%E7%AD%89%E5%BC%8F1%2Fa-1%2Fb%3Db-a%2Fab%2C%E5%A6%821%2F12%3D4-3%2F3%C3%974%3D1%2F3-1%2F4%2C%E6%A0%B9%E6%8D%AE%E4%B8%8A%E8%BF%B0%E7%AD%89%E5%BC%8F%E8%AE%A1%E7%AE%971%2B1%2F2%2B1%2F6%2B1%2F12%2B%E2%80%A6%2B1%2Fn%28n%2B1%29n%E4%B8%BA%E6%95%B4%E6%95%B0)
逆向运用不等式1/a-1/b=b-a/ab,如1/12=4-3/3×4=1/3-1/4,根据上述等式计算1+1/2+1/6+1/12+…+1/n(n+1)n为整数
逆向运用不等式1/a-1/b=b-a/ab,如1/12=4-3/3×4=1/3-1/4,根据上述等式计算1+1/2+1/6+1/12+…+1/n(n+1)
n为整数
逆向运用不等式1/a-1/b=b-a/ab,如1/12=4-3/3×4=1/3-1/4,根据上述等式计算1+1/2+1/6+1/12+…+1/n(n+1)n为整数
1/n(n+1)=1/n-1/(n+1)
1+1/2+1/6+1/12+…+1/n(n+1)=1+(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+[1/n-1/(n+1)]
=1+1-1/(n+1)=(2n+1)/(n+1)
1+1/2+1/6+1/12+…+1/n(n+1)
=1+1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1+1-1/(n+1)=(2n+1)/(n+1)