数列求和( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))最终答案是要原式

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数列求和(1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))(1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))最终答案是要原式

数列求和( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))最终答案是要原式
数列求和( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))
( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))
最终答案是要原式

数列求和( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))最终答案是要原式
an
=1/(2n-1)(2n+1)
=1/2[1/(2n-1)-1/(2n+1)]
Sn
=1/2[1-1/3]+1/2[1/3-1/5]+1/2[1/5-1/7]+...+1/2[1/(2n-3)-1/(2n-1)]+1/2[1/(2n-1)-1/(2n+1)]
=1/2[1-1/3+1/3-1/5+1/5-1/7+...+1/(2n-3)-1/(2n-1)+1/(2n-1)-1/(2n+1)]
=1/2[1-1/(2n+1)]
=n/(2n+1)

(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))=n/(2n+1)