A = \(\dfrac{36\times950+18\times726\times2+3\times324\times12}{1+3+5+7+...+27+29+31-152}\)

A = \(\dfrac{36\times950+36\times726+36\times324}{1+3+5+7+...+27+29+31-152}\)

MS = 1 + 3 + 5 +...+ 27 + 29 + 31 - 152

Xét dãy số: 1; 3; 5;...;27; 29; 31 là dãy số cách đều với khoảng cách là:  

                    3 - 1 = 2

Số số hạng của dãy số là: 

                 (31 - 1): 2 + 1 = 16

MS = (31 + 1) x 16 : 2 - 152 = 104

A = \(\dfrac{36\times\left(950+726+324\right)}{104}\)

A = \(\dfrac{36\times2000}{104}\)

A = \(\dfrac{9000}{13}\)

692 + 152 - 92

= (692 - 92) + 152

= 600 + 152

752

Tính nhanh 692+152−92

692+152−92=(692−92)+152=600+152=752 ( Đúng )

\(692+152-92=692-92-152=600-152=752\)( Sai )

\(C=\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}\)

\(C=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+\frac{2}{208}+\frac{2}{304}\)

\(C=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}+\frac{2}{16.19}\)

\(C=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\right)\)

\(C=\frac{2}{3}.\left(3-\frac{3}{4}+\frac{3}{4}-\frac{3}{7}+\frac{3}{7}-\frac{3}{10}+\frac{3}{10}-\frac{3}{13}+\frac{3}{13}-\frac{3}{16}+\frac{3}{16}-\frac{3}{19}\right)\)

\(C=\frac{2}{3}.\left(3-\frac{3}{19}\right)\)

\(C=\frac{2}{3}.\frac{54}{19}\)

\(C=\frac{36}{19}\)

mk sai bước cuối

\(C=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+\frac{1}{16}-\frac{1}{19}\right)\)

\(C=\frac{2}{3}.\left(1-\frac{1}{19}\right)\)

\(C=\frac{2}{3}.\frac{18}{19}\)

\(C=\frac{12}{19}\)

dấu . là nhân hay là phẩy vậy

Dấu . chắc là x ha :3 Lớp 6 nó thế mà :3333

5+ 5 + 5 + 5+ 5 + 5 +5+ 5 + 5 +5=5x10=50

25 + 25 + 25 + 25 + 25 + 25 +25 + 25=25x8=200

45 + 45 + 45 + 45 + 15 + 15 + 15 + 15=(45x4)+(15x4)=180+60=240

Ta có ( 10 a   –   5 ) 2   =   100 a 2  – 2.10a.5 + 25 = 100a(a – 1) + 25.

Nên 45 2  = 100.5.4 + 25 = 2025.

Tương tự:  15 2  = 225;  75 2  = 5625;  95 2  = 9025.

\(\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+\dfrac{1}{65}+\dfrac{1}{104}+\dfrac{1}{152}\\ =\dfrac{2}{4}+\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+\dfrac{2}{208}+\dfrac{2}{304}\\ =\dfrac{2}{3}\cdot\left(\dfrac{3}{4}+\dfrac{3}{28}+\dfrac{3}{70}+\dfrac{3}{130}+\dfrac{3}{208}+\dfrac{3}{304}\right)\\ =\dfrac{2}{3}\cdot\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}+\dfrac{3}{16\cdot19}\right)\\ =\dfrac{2}{3}\cdot\left(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{19}\right)\\ =\dfrac{2}{3}\cdot\left(1-\dfrac{1}{19}\right)\\ =\dfrac{2}{3}\cdot\dfrac{18}{19}\\ =\dfrac{12}{19}\)

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