1/1x2=1-1/2 1/2x3=1/2-1/3 若1/1x3+1/3x5+1/5x7+...+1/(2n-1)(2n+1)的值为17/35,求n的值!
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![1/1x2=1-1/2 1/2x3=1/2-1/3 若1/1x3+1/3x5+1/5x7+...+1/(2n-1)(2n+1)的值为17/35,求n的值!](/uploads/image/z/10166658-42-8.jpg?t=1%2F1x2%3D1-1%2F2+1%2F2x3%3D1%2F2-1%2F3+%E8%8B%A51%2F1x3%2B1%2F3x5%2B1%2F5x7%2B...%2B1%2F%EF%BC%882n-1%29%282n%2B1%29%E7%9A%84%E5%80%BC%E4%B8%BA17%2F35%2C%E6%B1%82n%E7%9A%84%E5%80%BC%21)
1/1x2=1-1/2 1/2x3=1/2-1/3 若1/1x3+1/3x5+1/5x7+...+1/(2n-1)(2n+1)的值为17/35,求n的值!
1/1x2=1-1/2 1/2x3=1/2-1/3 若1/1x3+1/3x5+1/5x7+...+1/(2n-1)(2n+1)的值为17/35,求n的值!
1/1x2=1-1/2 1/2x3=1/2-1/3 若1/1x3+1/3x5+1/5x7+...+1/(2n-1)(2n+1)的值为17/35,求n的值!
裂项求和
1/1x3+1/3x5+1/5x7+...+1/(2n-1)(2n+1)=17/35
1/2*[1-1/3+1/3-1/5+1/5-1/7+...+1/(2n-1)-1/(2n+1)]=17/35
1/2*[1-1/(2n+1)]=17/35
1/2*2n/(2n+1)=17/35
n/(2n+1)=17/35
17(2n+1)=35n
34n+17=35n
n=17