1+2+3+……+n=(1+n)*n/2;
X^(1/2)-Y^(1/2)=(X-Y)/(X^(1/2)+Y^(1/2));
根据以上原理原式可以转换成(1/(((1+1/n)/2)^0.5+(1-1/n)^0.5));
当n趋近于无限大时,1/n=0;
极限等于((2)^0.5)/2