\(\dfrac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\dfrac{2^{10}.3^9\left(3-1\right)}{2^9.3^{10}}=\dfrac{2^{10}.3^9.2}{2^9.3^{10}}=\dfrac{2^9.2.3^9.2}{2^9.3.3^9}=\dfrac{4}{3}\)

\(\dfrac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\dfrac{2^{10}.3^9\left(3-1\right)}{2^9.3^{10}}=\dfrac{2^{10}.3^9.2}{2^9.3^{10}}=\dfrac{2^{10}.2.3^9.2}{2^9.3.3^9}=\dfrac{4}{3}\)

\(\dfrac{-11^5.13^7}{11^5.13^8}=\dfrac{-1.11^5.13^7}{11^5.13^8}=-\dfrac{1}{13}\)

\(\dfrac{-11^5\cdot13^8}{11^5\cdot13^7}\)

\(=\dfrac{-11^5\cdot13^7\cdot13}{11^5\cdot13^7}\)

\(=\dfrac{-11^5\cdot13}{11^5}\)

\(=\dfrac{11^5\cdot\left(-13\right)}{11^5}\)

\(=-13\)

\(P=2.5+5.8+8.11+...+101.104\)

\(\Rightarrow9P=2.5.9+5.8.9+8.11.9+...+101.104.9\)

\(\Rightarrow9P=2.5.9+5.8.\left(11-2\right)+8.11.\left(14-5\right)+...+101.104.\left(107-98\right)\)

\(\Rightarrow9P=2.5.9-2.5.8+5.8.11-5.8.11+8.11.14+...-98.101.104+101.104.107\)

\(\Rightarrow9P=2.5.9-2.5.8+101.104.107\)

\(\Rightarrow9P=1123938\)

\(\Rightarrow P=124882\)

Giúp em nhanh với

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 = \(\dfrac{1215}{1309}\)