\(A=\dfrac{1}{1\cdot6}-\dfrac{1}{6\cdot11}-\dfrac{1}{11\cdot16}-\dfrac{1}{16\cdot21}-...-\dfrac{1}{46\cdot51}\)

\(=\dfrac{1}{6}-\left(\dfrac{1}{6\cdot11}+\dfrac{1}{11\cdot16}+\dfrac{1}{16\cdot21}+...+\dfrac{1}{46\cdot51}\right)\)

\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{5}{6\cdot11}+\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{46\cdot51}\right)\)

\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{46}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{6}-\dfrac{1}{5}\left(\dfrac{1}{6}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{6}-\dfrac{1}{5}\cdot\dfrac{5}{34}\)

\(=\dfrac{1}{6}-\dfrac{1}{34}\)

\(=\dfrac{7}{51}\)

Vậy \(A=\dfrac{7}{51}\)

\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{46.51}\)

\(=\frac{1}{5}.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{46.51}\right)\)

\(=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{46}-\frac{1}{51}\right)\)

\(=\frac{1}{5}.\left(1-\frac{1}{51}\right)\)

\(=\frac{1}{5}.\left(\frac{51}{51}-\frac{1}{51}\right)\)

\(=\frac{1}{5}.\frac{50}{51}\)

\(=\frac{10}{51}\)

Chúc bạn học tốt !!! 

=1/5.(1-1/51)

=1/5.50/51

=10/51

Đặt \(A=\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{46\cdot51}\)

\(5A=5\left(\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{46\cdot51}\right)\)

\(5A=\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{5}{46\cdot51}\)

\(5A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{46}-\frac{1}{51}\)

\(5A=1-\frac{1}{51}\)

\(5A=\frac{50}{51}\Rightarrow A=\frac{50}{51}:5\Rightarrow A=\frac{10}{51}\)

\(=5\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{101\cdot106}\right)\\ =5\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\\ =5\left(1-\dfrac{1}{106}\right)=5\cdot\dfrac{105}{106}=\dfrac{525}{106}\)

522+947=1469

522+741=1263

522+852=1374

963+789=1752

123+456=579

456+789=1245

k mik nhé bn!!

bạn dùng máy tính tính đi

dat ra cho vui ma?

Lời giải:
\(=-5^{22}-(-222-(-122-100+5^{22}+2022))\)

\(=-5^{22}-(-222+122+100-5^{22}-2022)\)

\(=-5^{22}+222-122-100+5^{22}+2022\)

\(=(-5^{22}+5^{22})+222-(122+100)+2022=0+222-222+2022=2022\)

Ta có: - 19 + (- 513) = - (19 + 513 )= - 532

Chọn (B) -532.

Bài 1:

\(=-5^{22}+222+[-122-(100-5^{22})+2022]\)

\(=-5^{22}+222-122-100+5^{22}+2022\\ =(-5^{22}+5^{22})+(222-122-100)+2022\\ =0+0+2022=2022\)

Bài 2:

$2n^2+n-6\vdots 2n+1$

$\Rightarrow n(2n+1)-6\vdots 2n+1$

$\Rightarrow 6\vdots 2n+1$

$\Rightarrow 2n+1\in Ư(6)$

Mà $2n+1$ lẻ nên $2n+1\in \left\{\pm 1; \pm 3\right\}$

$\Rightarrow n\in \left\{0; -1; 1; -2\right\}$

\(\overline{ab9}=\overline{ab}+522\)

\(\Rightarrow10.\overline{ab}+9=\overline{ab}+522\)

\(\Rightarrow10\overline{ab}-\overline{ab}=522-9\)

\(\Rightarrow9\overline{ab}=513\)

\(\Rightarrow\overline{ab}=\dfrac{513}{9}=57\)

Vậy số ab là số 57

phep tinh do la:9468-8946=522

abc8-8abc=522

10xabc+8-8000+abc=522

10xabc-abc-8000-8=522

9xabc-7992=522

9xabc=522+7992

9xabc=8514

abc=8514:9

abc=946

​Tick nha ủng hộ mình lên 90 với !!!!!!!!!!!!!!!!!!!!!!

Ta thấy: Hàng đơn vị số thứ nhất có chữ số là 8, suy ra C của hai số phải là 6 vì 8-6=2.

Giờ ta có: ab68-8ab6=522, thì B phải là 4 để 6-4=2

a468-8a46=522, số A phải là 9 vì 9468-8946=522, bạn cứ kiểm tra bằng máy tính là xong