方程1/3+1/(3+5)+1/(3+5+7)+...+1/(3+5+7+...+2n+1)=36/55
问题描述：
方程1/3+1/(3+5)+1/(3+5+7)+...+1/(3+5+7+...+2n+1)=36/55
求n的正整数解
答
1/3+1/(3+5)+1/(3+5+7)+...+1/(3+5+7+...+2n+1)=1/(1*3)+1/(2*4)+1/(3*5)+...+1/(n*(n+2))=(1-1/3+1/2-1/4+1/3-1/5+...+1/n-1/(n+2))/2=(1+1/2-1/(n+1)-1/(n+2))/2=36/55n=9