Question

tính

(100 + \(\frac{99}{2}+\frac{98}{3}+...+\frac{1}{100}\) ) : (\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{101}\) ) - 2 =?

hộ thêm câu này nữa m.n ơi 

Answer 1

ta có:

\(\left(100+\frac{99}{2}+\frac{98}{3}+...+\frac{1}{100}\right):\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{101}\right)-2\)

=\(\left(1+\frac{99}{2}+1+\frac{98}{3}+1+...+\frac{1}{100}+1\right):\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{101}\right)-2\)

=\(\left(\frac{101}{101}+\frac{101}{2}+\frac{101}{3}+...+\frac{101}{100}\right):\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}+\frac{1}{101}\right)-2\)

=\(101\left(\frac{1}{101}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right):\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}+\frac{1}{101}\right)-2\)

=101-2=99