1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,

题目

1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,

答案

1/1*1/3+1/3*1/5+1/5*1/7+.+1/49*1/51+...+1/(2n-1)(2n+1)=1/2[1/1-1/3+1/3-1/5+1/5-1/7+.+1/49-1/51+...+1/(2n-1)-1/(2n+1)]=1/2[1-1/(2n+1)]=n/(2n+1)当n=25时,1/1*1/3+1/3*1/5+1/5*1/7+.+1/49*1/51+...+1/(2n-1)(...