a; \(\dfrac{6}{x}\) < \(\dfrac{x}{7}\) < \(\dfrac{8}{x}\)

    vì \(x\) \(\in\) N* ta có: 6.7 < \(x.x\) < 7.8

                             42 < \(x^2\) < 56

                            \(x^2\) = 49 

                           \(x\) = \(\pm\) 7

Vì \(x\) \(\in\) N*; \(x\) = 7

b;  \(\dfrac{x}{11}\) < \(\dfrac{12}{x}\) < \(\dfrac{x}{9}\)

   9.12<   \(x^2\) < 11.12 

    108 < \(x^2\) < 132

            \(x^2\) = 121

            \(\left[{}\begin{matrix}x=-11\\x=11\end{matrix}\right.\)

    Vì \(x\in\) N*

   \(x\)  = 11

Giúp em nhanh với

...

7+(-x) = -19
-x = -19 - 7
-x = -26

...

S = 6³ + 6⁵ + 6⁷ + ... + 6¹⁰¹

6² x S = 6⁵ + 6⁷ + 6⁹ + ... + 6¹⁰³

36S-S = 6⁵ + 6⁷ + 6⁹ + ... + 6¹⁰³ - 6³ - 6⁵ - 6⁷ - ... - 6¹⁰¹

35S = 6¹⁰³ - 6³ 

S = ( 6¹⁰³ - 6³ ) : 35

CHÚC BẠN HỌC TỐT NHÉ!!

S = \(\dfrac{3}{1\times4}\) + \(\dfrac{3}{4\times7}\) + \(\dfrac{3}{7\times11}\) + \(\dfrac{3}{11\times14}\) + \(\dfrac{3}{14\times17}\)

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{4}{7.11}\) + \(\dfrac{3}{11.14}\) +\(\dfrac{3}{14.17}\) - \(\dfrac{1}{7.11}\)

S = \(\dfrac{1}{1}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{11}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{7.11}\)

S = \(\dfrac{1}{1}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\)

S =  \(\dfrac{16}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{1215}{1309}\)

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{3}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\)

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{4}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\) - \(\dfrac{1}{7.11}\)

S = \(\dfrac{1}{1}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\)  - \(\dfrac{1}{7}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{1}{1}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{16}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{1215}{1309}\)

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{3}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\)

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{4}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\) - \(\dfrac{1}{7.11}\)

S = \(\dfrac{1}{1}\)-\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{11}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\) 

S = 1 - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{16}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{1215}{1309}\)

Đề sai, như vậy không tính nhanh được nhé em!

Bạn xem đã viết đúng đề chưa nhỉ. Các thừa số đang cách nhau 3 đơn vị tự nhiên xuất hiện 7 x 11 có 2 thừa số cách nhau 4 đơn vị?

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{3}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\)

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{4}{7.11}\) - \(\dfrac{1}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\)

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{4}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\) - \(\dfrac{1}{7.11}\)

S = \(\dfrac{1}{1}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{11}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{1}{1}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{16}{17}\) - \(\dfrac{1}{77}\)

S = \(\dfrac{1215}{1309}\)