1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))=17/35求n的值

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1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))=17/35求n的值
1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))=17/35求n的值

1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))=17/35求n的值
1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))=17/35
1/2(1-1/3)+1/2(1/3-1/5)+……+1/2[1/(2n-1)-1/(2n+1)]=17/35
1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1)=34/35
1-1/(2n+1)=34/35
1/(2n+1)=1-34/35=1/35
2n+1=35
n=17