等差数列求和急1/1+1/(1+2)+1/(1+2+3).+1/(1+2+3+..N)
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等差数列求和急
1/1+1/(1+2)+1/(1+2+3).+1/(1+2+3+..N)
1/1+1/(1+2)+1/(1+2+3).+1/(1+2+3+..N)
![等差数列求和急1/1+1/(1+2)+1/(1+2+3).+1/(1+2+3+..N)](/uploads/image/z/1304866-10-6.jpg?t=%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E6%B1%82%E5%92%8C%E6%80%A51%2F1%2B1%2F%281%2B2%29%2B1%2F%281%2B2%2B3%29.%2B1%2F%281%2B2%2B3%2B..N%29)
原式=1+2/2*(2+1)+2/3*(3+1)+……+2/n(n+1)
=1+2(1/2-1/3+1/3-1/3+……+1/n-1/(n+1)
=1+1/4-1/2(n+1)
=(3-2n)/4(n+1)
=1+2(1/2-1/3+1/3-1/3+……+1/n-1/(n+1)
=1+1/4-1/2(n+1)
=(3-2n)/4(n+1)
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