若1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)的值为17/35,求n值

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若1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)的值为17/35,求n值

若1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)的值为17/35,求n值
若1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)的值为17/35,求n值

若1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)的值为17/35,求n值
首先要知道
1/(2n-1)(2n+1)=1/2[1/(2n-1)-1/(2n+1)],这样求和就方便求了
1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)
=1/2[1-1/3+1/3-1/5+1/5-1/7+...+1/(2n-1)-1/(2n+1)]
=1/2[(1-1/(2n+1)]=17/35
所以求得 n=17

1/1*3+1/3*5+1/5*7+……+1/(2n-1)(2n+1)
=[1 - 1/3 + 1/3 - 1/5 + 1/4=5 - 1/7 + ... + 1/(2n -1) - 1/(2n+1)]/2
=[1 - 1/(2n +1)]/2
= n/(2n+1) = 17/35
解得 n = 17