Question

1×3分之1+3×5分之1+5×7分之1+…+（2n-1）（2n+1）分之1的值为35分之17,求n的值.

Answer 1

n=17

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(2n/(2n+1))

=n/(2n+1)

=17/35

35n=17(2n+1)

35n=34n+17

n=17

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