\(\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+\frac{6}{130}\)

\(=\frac{6}{1x4}+\frac{6}{4x7}+\frac{6}{7x10}+\frac{6}{10x13}\)

\(=2\left(\frac{3}{1x4}+\frac{3}{4x7}+\frac{3}{7x10}+\frac{3}{10x13}\right)\)

\(=2\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}\right)\)

\(=2\left(1-\frac{1}{13}\right)\)

\(=2x\frac{12}{13}\)

\(=\frac{24}{13}\)

\(\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+\frac{6}{130}\)

\(=\frac{6}{1.4}+\frac{6}{4.7}+\frac{6}{7.10}+\frac{6}{10.13}\)

\(=2\left(\frac{3}{1.4}+\frac{3}{1.7}+\frac{3}{7.10}+\frac{3}{10.13}\right)\)

\(=2\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}\right)\)

\(\Leftrightarrow2=\left(1-\frac{1}{13}\right)\)

\(=2.\frac{12}{13}\)

\(=\frac{24}{13}\)

Bạn ơi, có chắc là 6/280 ở cuối không.

Trả lời nhanh để mink giải câu này cho

lộn \(\frac{6}{208}\) chứ ko phải 6/ 280

\(\frac{6}{1.4}+\frac{6}{4.7}+\frac{6}{7.10}+.....+\frac{6}{13.16}\)

Ta có công thức \(\frac{a}{b.c}=\frac{a}{c-b}.\left(\frac{1}{b}-\frac{1}{c}\right)\)

Dựa vào công thức ta có :

\(\frac{6}{1.4}=\frac{6}{3}.\left(1-\frac{1}{4}\right)\)

\(\frac{6}{4.7}=\frac{6}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)\)

.....................................

\(\frac{6}{13.16}=\frac{6}{3}.\left(\frac{1}{13}-\frac{1}{16}\right)\)

\(\Rightarrow\)\(\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+......+\frac{6}{208}=\frac{6}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{13}-\frac{1}{16}\right)\)

\(\Rightarrow\)\(\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+.....+\frac{6}{208}=\frac{6}{3}.\left(1-\frac{1}{16}\right)=\frac{6}{3}.\left(\frac{15}{16}\right)=\frac{15}{8}\)

Mink chắc chắn, ai thấy đúng thì ủng hộ mink nha !!!

Bài 1: 

\(=\dfrac{1}{\left(x+1\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+7\right)}+\dfrac{1}{\left(x+7\right)\left(x+10\right)}+\dfrac{1}{\left(x+10\right)\left(x+13\right)}+\dfrac{1}{\left(x+13\right)\left(x+16\right)}\)

\(=\dfrac{1}{3}\left(\dfrac{3}{\left(x+1\right)\left(x+4\right)}+\dfrac{3}{\left(x+4\right)\left(x+7\right)}+\dfrac{3}{\left(x+7\right)\left(x+10\right)}+\dfrac{3}{\left(x+10\right)\left(x+13\right)}+\dfrac{3}{\left(x+13\right)\cdot\left(x+16\right)}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{x+1}-\dfrac{1}{x+4}+\dfrac{1}{x+4}-\dfrac{1}{x+7}+\dfrac{1}{x+7}-\dfrac{1}{x+10}+\dfrac{1}{x+10}-\dfrac{1}{x+13}+\dfrac{1}{x+13}-\dfrac{1}{x+16}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{x+1}-\dfrac{1}{x+16}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{x+16-x-1}{\left(x+1\right)\left(x+16\right)}=\dfrac{5}{\left(x+1\right)\left(x+16\right)}\)

Bài 2: 

\(\Leftrightarrow a^2-2a+1+b^2+4b+4+4c^2-4c+1=0\)

\(\Leftrightarrow\left(a-1\right)^2+\left(b+4\right)^2+\left(2c-1\right)^2=0\)

Dấu '=' xảy ra khi a=1; b=-4; c=1/2

c)  \(A=\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+\frac{6}{130}+\frac{6}{208}\) 

\(=\frac{6}{1.4}+\frac{6}{4.7}+\frac{6}{7.10}+\frac{6}{10.13}+\frac{6}{13.16}\) 

\(=2\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)

\(=2\left(1-\frac{1}{16}\right)\) 

\(=2.\frac{15}{16}\) 

\(=\frac{15}{8}\) 

Vậy A=\(\frac{15}{8}\)

a) \(\frac{3^2}{1.4}+\frac{3^2}{4.7}+\frac{3^2}{7.10}+...+\frac{3^2}{97.100}\)

\(=3\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\right)\)

\(=3\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)

\(=3\left(1-\frac{1}{100}\right)\)

\(=3.\frac{99}{100}=\frac{297}{100}\)

\(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)

\(=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{10}{20}-\frac{1}{20}\)

\(=\frac{9}{20}\)

A = \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{56}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{7.8}\)

  \(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{7}-\frac{1}{8}\)

  \(=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

B = \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)

  \(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)

  \(=1-\frac{1}{13}=\frac{12}{13}\)

\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{56}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{7.8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

\(B=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)

\(=1-\frac{1}{13}=\frac{12}{13}\)

A=\(\frac{1}{6}\)+\(\frac{1}{12}\)+......+\(\frac{1}{56}\)

A=\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+...+\(\frac{1}{7.8}\)

A=\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+....+\(\frac{1}{7}\)-\(\frac{1}{8}\)

A=\(\frac{1}{2}\)-\(\frac{1}{8}\)=\(\frac{3}{8}\)

B=\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+...+\(\frac{2}{11.13}\)

B=1-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+....+\(\frac{1}{11}\)-\(\frac{1}{13}\)

B=1-\(\frac{1}{13}\)=\(\frac{12}{13}\)

C=\(\frac{3}{4}\)+\(\frac{3}{28}\)+....+\(\frac{3}{304}\)

C=\(\frac{3}{1.4}\)+\(\frac{3}{4.7}\)+..+\(\frac{3}{16.19}\)

Rồi bạn cũng tách ra như câu A và câu B

1/2A=1/2(6/4+6/28+6/70+6/130+6/208)

       = 3/4+3/28+3/70+3/130+3/208

       = 1-1/4+1/4-1/7+..................-1/16

       =1-1/16

       =15/16 => A=15/8

b) D = \(\frac{3}{4}+\frac{3}{8}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)

    D =  \(3\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+\frac{1}{208}+\frac{1}{304}\right)\)

    D = \(3\left(\frac{1}{1x4}+\frac{1}{4x7}+\frac{1}{7x10}+\frac{1}{10x13}+\frac{1}{13x16}+\frac{1}{16x19}\right)\)

    D = \(\frac{1}{1}-\frac{1}{19}=\frac{18}{19}\)

Chắc vậy

chịu thôi

B=64,8

a,

A = 5.(2² . 3² )⁹. (2²)⁶ - 2. (2².3)¹⁴.3⁴ / 5.2²⁸.3¹⁸ - 7.2²⁹.3¹⁸

A = 5.2¹⁸.3¹⁸.2¹² - 2. 2^28. 3¹⁴. 3⁴ / 5. 2²⁸. 3¹⁸ - 7. 2²⁹. 3¹⁸

A = 5.2³⁰.3¹⁸ - 2²⁹. 3¹⁸ /  5.2 ²⁸.3¹⁸ - 7.2²⁹. 3¹⁸

A = 2²⁹. 3¹⁸(5.2-1) / 2²⁸. 3¹⁸ (5 -7.2)

A = 2.9 / -9 = -2

Vậy A = -2

b,

B =81.( 12 - 12/7- 12/289 - 12/85 /  4 - 4/7 - 4/289 - 4/85 :

5 + 5/13 + 5/169 + 5/91 /  6 + 6/13 + 6/169 + 5/91 ) x 158158158

B = 81.[ 12.( 1 - 1/7 - 1/289 - 1/85) / 4.( 1 - 1/7 - 1/289 - 1/85 :

5.(1 + 1/13 + 1/169 + 1/91) / 6.(1+ 1/13 +1/169 + 1/91)] . 2/9

B = 81.[ 3 : 5/6 ] .2/9

B = 81.18/5 . 2/9

B = 1458/5 . 2/9

B = 324/5.

Vậy B = 324/5

CHÚC HỌC TỐT

\(a)\) \(A=\frac{5\left(2^2.3^2\right)^9.\left(2^2\right)^6-2\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)

\(A=\frac{2^{30}.3^{18}.5-2^{29}.3^{18}}{2^{28}.3^{18}.5-2^{29}.3^{18}.7}\)

\(A=\frac{2^{29}.3^{18}\left(2.5-1\right)}{2^{28}.3^{18}\left(5-2.7\right)}\)

\(A=\frac{2\left(10-1\right)}{5-14}\)

\(A=\frac{2.9}{-9}\)

\(A=-2\)

Vậy \(A=-2\)

\(b)\) \(B=81.\left[\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right].\frac{158158158}{711711711}\)

\(B=81.\left[\frac{12\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}{4\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}:\frac{5\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}{6\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}\right].\frac{158158158}{711711711}\)

\(B=81.\left[\frac{12}{4}:\frac{5}{6}\right].\frac{2}{9}\)

\(B=81.\frac{18}{5}.\frac{2}{9}\)

\(B=\frac{324}{5}\)

Vậy \(B=\frac{324}{5}\)

Chúc bạn học tốt ~ ( mỏi tay qué >_< )