1/2+1/6+1/12+1/20+...+1/90 这道算式如何简便计算?
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![1/2+1/6+1/12+1/20+...+1/90 这道算式如何简便计算?](/uploads/image/z/66768-24-8.jpg?t=1%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B...%2B1%2F90+%E8%BF%99%E9%81%93%E7%AE%97%E5%BC%8F%E5%A6%82%E4%BD%95%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%3F)
1/2+1/6+1/12+1/20+...+1/90 这道算式如何简便计算?
1/2+1/6+1/12+1/20+...+1/90 这道算式如何简便计算?
1/2+1/6+1/12+1/20+...+1/90 这道算式如何简便计算?
1/2+1/6+1/12+1/20+...+1/90
=1/2+(1/2-1/3)+(1/3-1/4)...+(1/9-1/10)
=1/2+1/2-1/10
=9/10
1/2+1/6+1/12+1/20+...+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10
=1-1/10
=9/10
1/2+1/6+1/12+1/20+...+1/90
观察可知通项为1/x*(x+1)
即:1/x-1/(x+1)
1/2+1/6+1/12+1/20+...+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10
=1-1/10
=9/10
1/2+1/6+1/12+1/20+...+1/90 =1/2+1/2*3+1/3*4+...+1/9*10=1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10=1/2+1/2-1/10=9/10
分母是可以分解为 两个连续自然数得乘积
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
因此可以得出 1-1/2+1/2-1/3+1/3-1/4+。。。。。。+1/9-1/10
=1-1/10=9/10