sin((n+1)^(1/2))-sin(n^(1/2)) = 2sin[((n+1)^(1/2) - n^(1/2))/2]* cos[((n+1)^(1/2) + n^(1/2))/2]
因为|cos[((n+1)^(1/2) + n^(1/2))/2]|≤1,
sin[((n+1)^(1/2) - n^(1/2))/2]=sin[1/2 * 1/((n+1)^(1/2) + n^(1/2))]→0,n→∞,
所以sin((n+1)^(1/2))-sin(n^(1/2))→0,n→∞.