1/(根号2+1)+1/(根号3+根号2)+1/(2+根号3)+……+1/(根号2015+根号2014)(根号2015+1)=
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 07:12:02
![1/(根号2+1)+1/(根号3+根号2)+1/(2+根号3)+……+1/(根号2015+根号2014)(根号2015+1)=](/uploads/image/z/531906-42-6.jpg?t=1%2F%EF%BC%88%E6%A0%B9%E5%8F%B72%2B1%EF%BC%89%2B1%2F%EF%BC%88%E6%A0%B9%E5%8F%B73%2B%E6%A0%B9%E5%8F%B72%EF%BC%89%2B1%2F%EF%BC%882%2B%E6%A0%B9%E5%8F%B73%EF%BC%89%2B%E2%80%A6%E2%80%A6%2B1%2F%EF%BC%88%E6%A0%B9%E5%8F%B72015%2B%E6%A0%B9%E5%8F%B72014%EF%BC%89%EF%BC%88%E6%A0%B9%E5%8F%B72015%2B1%EF%BC%89%3D)
1/(根号2+1)+1/(根号3+根号2)+1/(2+根号3)+……+1/(根号2015+根号2014)(根号2015+1)=
1/(根号2+1)+1/(根号3+根号2)+1/(2+根号3)+……+1/(根号2015+根号2014)(根号2015+1)=
1/(根号2+1)+1/(根号3+根号2)+1/(2+根号3)+……+1/(根号2015+根号2014)(根号2015+1)=
考虑原数列的通项1/[根号(n+1)+n],分式有理化:
1/[根号(n+1)+根号n]= 根号(n+1)-根号n
所以原式= (根号2-1)+ (根号3-根号2)+ (根号4-根号3)+...+(根号n-根号(n-1))= 根号n- 1