√n² <√(n²+1) <√[n²+1+1/(4n²)]
即 n <√(n²+1) < n + 1/(2n)
lim(n→∞)sin(nπ)= 0
lim(n→∞)sin{[n+1/(2n)]π} = lim(n→∞) [sin(nπ)cos(π/2n)+ cos(nπ)sin(π/2n)]
= 0
∴lim(n→∞)sin{[√(n²+1)]*π} = 0
√n² <√(n²+1) <√[n²+1+1/(4n²)]
即 n <√(n²+1) < n + 1/(2n)
lim(n→∞)sin(nπ)= 0
lim(n→∞)sin{[n+1/(2n)]π} = lim(n→∞) [sin(nπ)cos(π/2n)+ cos(nπ)sin(π/2n)]
= 0
∴lim(n→∞)sin{[√(n²+1)]*π} = 0