1/3+1/(3+3)+1/(3+3+5)+1/(3+3+5+7)+1/(3+3+5+7+9)+.+1/(3+3+5+7+.+2n-1)

问题描述:

1/3+1/(3+3)+1/(3+3+5)+1/(3+3+5+7)+1/(3+3+5+7+9)+.+1/(3+3+5+7+.+2n-1)

Step 1:第n项 等于 1/(3+(2n-1))*((2n-1-3)/2-1)/2 = 1/(n^2+2)
Step 2:1/(n^2+2) Step 3:1/ (n^2-1)