lim x→n (√n+1-√n)*√(n+1/2)

问题描述:

lim x→n (√n+1-√n)*√(n+1/2)
lim x n→∞ (√n+1-√n)*√(n+1/2)

lim x n→∞ (√n+1-√n)*√(n+1/2)
乘以(√n+1+√n)再除以(√n+1+√n)得
lim x n→∞ (√n+1-√n)*√(n+1/2)=lim x n→∞√(n+1/2)/(√n+1+√n),分子分母同除以√n
原式=lim x n→∞√(1+1/2n)/(√n+1/n+1)=1/(1+1)=1/2.核心就是构造1/n