1/3 +1/15 +1/35 +……+1/(2n-1)(2n+1)=17/35求n的值

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1/3+1/15+1/35+……+1/(2n-1)(2n+1)=17/35求n的值1/3+1/15+1/35+……+1/(2n-1)(2n+1)=17/35求n的值1/3+1/15+1/35+……+1

1/3 +1/15 +1/35 +……+1/(2n-1)(2n+1)=17/35求n的值
1/3 +1/15 +1/35 +……+1/(2n-1)(2n+1)=17/35
求n的值

1/3 +1/15 +1/35 +……+1/(2n-1)(2n+1)=17/35求n的值
1/(2n-1)(2n+1)
=[1/(2n-1)-1/(2n+1)]/2
所以
1/3 +1/15 +1/35 +……+1/(2n-1)(2n+1)
=1/2[1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1)]
=1/2[1-1/(2n+1)]
=17/35
解得n=17

1/(2n-1)(2n+1)=1/2[1/(2n-1)-1/(2n+1)]
1/3 +1/15 +1/35 +……+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)]
=n/(2n+1)=17/35
n=17

=1/2(1-1/3+1/3-1/5+......+1/2n-1-1/2n+1)
=1/2[1-1/(2n+1)]=17/35
1/2*2n/(2n+1)=17/35
35n=34n+17
n=17

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
得:n=17