数列求和( 1/1*3)+(1/3*5)+(1/5*7)+...+(1/(2n-1)(2n+1))( 1/1*3)+(1/3*5)_数学解答

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

人气：458 ℃　时间：2020-01-30 12:32:49

解答

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)...