Có 100 trăm cặp mà mỗi cặp bằng -1

Lấy: 100 .(-1)=-100

Ta có:

\(S=\frac{4}{1.3}+\frac{16}{3.5}+\frac{36}{5.7}+........+\frac{2500}{49.51}\)

a) (-4).(-3).(-125). 25.(-8)

= [ -8.( -125)] . (-4.25) . (-3)

=1000. (-100).3

= - 100000 .3

= - 300000

b) 136. (- 47 ) + 36.47

= -136 .47 +36.47

=47.( -136+36)

= 47. ( -100)

= -4700

d)  125.(-24) + 24.125

= 125. ( -24+24)

= 125. 0

=0

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\)

\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{9}\right)\)

\(=\frac{1}{2}.\frac{8}{9}\)

\(=\frac{4}{9}\)

#)Giải :

\(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\)

\(\Rightarrow2S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\)

\(\Rightarrow2S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\)

\(\Rightarrow2S=1-\frac{1}{9}=\frac{8}{9}\)

\(S=\frac{8}{9}:2=\frac{4}{9}\)

             #~Will~be~Pens~#

S=\(\frac{1}{1×3}+\frac{1}{3×5}+\frac{1}{5×7}+\frac{1}{7×9}\)

S=\(\frac{1.2}{\left(1.3\right).2}+\frac{1.2}{\left(3.5\right).2}+\frac{1.2}{\left(5.7\right).2}+\frac{1.2}{\left(7.9\right).2}\)

S=\(\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)\)

S= \(\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)\)

S= \(\frac{1}{2}.\left(1-\frac{1}{9}\right)\)

S= 1/2 . 8/9

S = 4/9

Lưu ý : "." có nghĩa là dấu nhân , lên cấp 2 bạn sẽ được học  

A=(-3/4+2/3).11/9+(-1/4+1/3):|-9/11|

\(=\left(-\frac{3}{4}+\frac{2}{3}\right).\frac{11}{9}+\left(-\frac{1}{4}+\frac{1}{3}\right).\frac{11}{9}\)

\(=\frac{11}{9}\left(-\frac{3}{4}+\frac{2}{3}-\frac{1}{4}+\frac{1}{3}\right)\)

\(=\frac{11}{9}\left(-1+1\right)\)

\(=\frac{11}{9}.0\)

=0

4/5x7 + 4/7x9 + 4/9x11 + ... + 4/50x61

= 2x(2/5x7 + 2/7x9 + 2/9x11 + ... + 2/59x61)

= 2x [(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+...+(1/59-1/61)]

= 2x(1/5-1/61)

= 2x 56/305

= 112/305

nhận giá trị âm tức là giá trị của biểu thức nhỏ hơn 0 và ngược lại!

a) \(15-3x< 0\)

\(\Leftrightarrow-3x< -15\)

\(\Leftrightarrow3x>5\)

b) \(27x+9< 0\)

\(\Leftrightarrow27x< -9\)

\(\Leftrightarrow x< -\frac{1}{3}\)

c) \(2y^2-4x< 0\)

\(\Leftrightarrow2\cdot\left(y^2-2x\right)< 0\)

\(\Leftrightarrow y^2-2x< 0\)

......