探究1/1*2+1/2*3+1/3*4+...+1/n(n+1)= 若1/1*3+1/3*5+1/5*7+.1/(2n-
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探究1/1*2+1/2*3+1/3*4+...+1/n(n+1)= 若1/1*3+1/3*5+1/5*7+.1/(2n-1)(2n+1)的值为17/35,求n的值
![探究1/1*2+1/2*3+1/3*4+...+1/n(n+1)= 若1/1*3+1/3*5+1/5*7+.1/(2n-](/uploads/image/z/20024876-20-6.jpg?t=%E6%8E%A2%E7%A9%B61%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B...%2B1%2Fn%28n%2B1%29%3D+%E8%8B%A51%2F1%2A3%2B1%2F3%2A5%2B1%2F5%2A7%2B.1%2F%282n-)
*3+1/3*4+...+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/1*3+1/3*5+1/5*7+.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
1-1/(2n+1)=34/35
1/(2n+1)=1/35
2n+1=35
n=17
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/1*3+1/3*5+1/5*7+.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
1-1/(2n+1)=34/35
1/(2n+1)=1/35
2n+1=35
n=17
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