数列{根号( n+2)-2根号(n+1)+根号n},求前n项和的极限
问题描述:
数列{根号( n+2)-2根号(n+1)+根号n},求前n项和的极限
答
a(n) = [(n+2)^(1/2) - (n+1)^(1/2)] - [(n+1)^(1/2) - n^(1/2)],s(n) = a(1)+a(2)+...+a(n-1)+a(n)=[3^(1/2)-2^(1/2)]-[2^(1/2)-1^(1/2)] + [4^(1/2)-3^(1/2)]-[3^(1/2)-2^(1/2)] + ...+[(n+1)^(1/2)-n^(1/2)]-[n^(...