Question

Thưc hiện phép tính

\(\frac{1+\frac{1}{3}+\frac{1}{5}+...\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{97.3}+\frac{1}{99.1}}\)

Answer 1

Tử số = 1 + 1/3 + 1/5 + ... + 1/97 + 1/99

= (1 + 1/99) + (1/3 + 1/97) + ... + (1/49 + 1/51)

= 100/1.99 + 100/3.97 + ... + 100/49.51

= 100.(1/1.99 + 1/3.97 + ... + 1/49.51)

Mẫu số = 1/1.99 + 1/3.97 + 1/5.95 + ... + 1/97.3 + 1/99.1

= 2.(1/1.99 + 1/3.97 + 1/5.95 + ... + 1/49.51)

=> phân số đề bài cho = 100/2 = 50

Answer 2

                    Ta có :

               \(\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{97.3}+\frac{1}{99.1}}\)

              \(=\frac{\left(1+\frac{1}{99}\right)+\left(\frac{1}{3}+\frac{1}{97}\right)+...+\left(\frac{1}{49}+\frac{1}{51}\right)}{2.\left(\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{49.51}\right)}\)

             \(=\frac{\frac{100}{1.99}+\frac{100}{3.97}+...+\frac{100}{49.51}}{2.\left(\frac{1}{1.99}+\frac{1}{3.97}+...+\frac{1}{49.51}\right)}\)

             \(=\frac{100.\left(\frac{1}{1.99}+\frac{1}{3.97}+...+\frac{1}{49.51}\right)}{2.\left(\frac{1}{1.99}+\frac{1}{3.97}+...+\frac{1}{49.51}\right)}\)

             \(=\frac{100}{2}=50\)

            Ủng hộ mk nha !!! ^_^

Answer 3

Tính B=(1/2+1/3+1/4+....+1/100)/(99/1+98/2+97/3+...+1/99)