Question

Chứng minh rằng các tổng sau lớn hơn 1 a)M= 3/8+3/15+3/7 b) N= 41/90+31/72+21/40+-11/45+-1/36

Answer 1

a) M = \(\frac{3}{8}+\frac{3}{15}+\frac{3}{7}\)

= 3 x( \(=\frac{1}{8}+\frac{1}{15}+\frac{1}{7}\) )

= 3 x \(\frac{105+56+120}{8x15x7}\)

= 3 x \(\frac{281}{3x5x8x7)\

= \(\frac{281}{280}\) > 1

Phần b tương tự nha !!

Answer 2

Chỗ kia mk viết nhầm !!

= 3 x \(\frac{281}{3x5x8x7}\)

Answer 3

a. Có \(M=\frac{3}{8}+\frac{3}{15}+\frac{3}{7}\)

\(=3.\left(\frac{1}{8}+\frac{1}{15}+\frac{1}{7}\right)\)

\(=3.\left(\frac{15.7}{8.15.7}+\frac{8.7}{8.15.7}+\frac{8.5}{8.15.7}\right)\)

\(=3.\left(\frac{15.7+8.7+8.5}{8.15.7}\right)\)

\(=3.\frac{281}{8.3.5.7}\)

\(=\frac{281}{280}\)

Mà \(\frac{281}{280}>1\)

Vậy M > 1

b. \(\frac{41}{90}+\frac{31}{72}+\frac{21}{40}+-\frac{11}{45}+-\frac{1}{36}\)

\(=\left(\frac{41}{90}+-\frac{11}{45}+\frac{41}{90}\right)+\left(\frac{31}{72}+-\frac{1}{36}\right)\)

\(=\frac{2}{3}+\frac{29}{72}\)

\(=\frac{77}{72}\)

Mà \(\frac{77}{72}>1\)

Vậy N > 1