Đêg bài là j vậy nguyen cong phuong

a: \(1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+...+\dfrac{1}{16}\left(1+2+3+...+16\right)\)

\(=1+\dfrac{1}{2}\cdot\dfrac{2\cdot3}{2}+\dfrac{1}{3}\cdot\dfrac{3\cdot4}{2}+...+\dfrac{1}{16}\cdot\dfrac{16\cdot17}{2}\)

\(=1+\dfrac{3}{2}+\dfrac{4}{2}+...+\dfrac{17}{2}\)

\(=\dfrac{1}{2}\left(2+3+4+...+17\right)\)

\(=\dfrac{1}{2}\cdot152=76\)

b: Sửa đề: \(\left[\left(\dfrac{2}{193}-\dfrac{3}{386}\right)\cdot\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{1931}+\dfrac{11}{3862}\right)\cdot\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\left(\dfrac{2}{193}\cdot\dfrac{193}{17}-\dfrac{3}{386}\cdot\dfrac{193}{17}+\dfrac{33}{34}\right):\left[\dfrac{7}{1931}\cdot\dfrac{1931}{25}+\dfrac{11}{3862}\cdot\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\left(\dfrac{2}{17}-\dfrac{3}{34}+\dfrac{33}{34}\right):\left(\dfrac{7}{25}+\dfrac{11}{50}+\dfrac{9}{2}\right)\)

\(=\left(\dfrac{2}{17}+\dfrac{30}{34}\right):\dfrac{14+11+225}{50}\)

\(=1\cdot\dfrac{50}{250}=1\cdot\dfrac{1}{5}=\dfrac{1}{5}\)

c: Sửa đề: \(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{\dfrac{2}{3}-\dfrac{2}{7}-\dfrac{2}{13}}\cdot\dfrac{\dfrac{3}{4}-\dfrac{3}{16}-\dfrac{3}{64}-\dfrac{3}{256}}{1-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}}+\dfrac{5}{8}\)

\(=\dfrac{1\left(\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}\right)}{2\left(\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}\right)}\cdot\dfrac{\dfrac{3}{4}\left(1-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}\right)}{1-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}}+\dfrac{5}{8}\)

\(=\dfrac{1}{2}\cdot\dfrac{3}{4}+\dfrac{5}{8}=\dfrac{3}{8}+\dfrac{5}{8}=1\)

d: \(\dfrac{0,125-\dfrac{1}{5}+\dfrac{1}{7}}{0,375-\dfrac{3}{5}+\dfrac{3}{7}}+\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-0,2}{\dfrac{3}{4}+0,5-\dfrac{3}{10}}\)

\(=\dfrac{\dfrac{1}{8}-\dfrac{1}{5}+\dfrac{1}{7}}{\dfrac{3}{8}-\dfrac{3}{5}+\dfrac{3}{7}}+\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{5}}{\dfrac{3}{4}+\dfrac{3}{6}-\dfrac{3}{10}}\)

\(=\dfrac{\dfrac{1}{8}-\dfrac{1}{5}+\dfrac{1}{7}}{3\left(\dfrac{1}{8}-\dfrac{1}{5}+\dfrac{1}{7}\right)}+\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{5}}{\dfrac{3}{2}\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{5}\right)}\)

\(=\dfrac{1}{3}+1:\dfrac{3}{2}=1\)

1) \(\frac{5}{8}.\frac{7}{3}-\frac{5}{2}.\frac{1}{8}=\frac{5}{8}.\frac{7}{3}-\frac{5}{8}.\frac{1}{2}=\frac{5}{8}\left(\frac{7}{3}-\frac{1}{2}\right)=\frac{5}{8}.\frac{11}{6}=\frac{55}{48}\)

2) \(\frac{21}{10}.\frac{3}{4}-\frac{21}{10}.\frac{3}{4}=\frac{21}{10}\left(\frac{3}{4}-\frac{3}{4}\right)=\frac{21}{10}.0=0\)

3) \(\frac{-4}{11}:\frac{-6}{11}=\frac{-4}{11}.\frac{-11}{6}=\frac{-4.\left(-11\right)}{11.6}=\frac{-4.\left(-1\right)}{1.6}=\frac{4}{6}=\frac{2}{3}\)

4)\(\frac{2}{7}.\frac{14}{3}-1=\frac{2.14}{7.3}-1=\frac{2.2}{1.3}-1=\frac{4}{3}-1=\frac{1}{3}\)

5)\(\frac{4}{7}:\left(\frac{1}{5}.\frac{4}{7}\right)=\frac{4}{7}:\frac{4}{35}=\frac{4}{7}.\frac{35}{4}=\frac{4.35}{7.4}=\frac{1.5}{1.1}=5\)

6) \(\frac{12}{7}.\frac{7}{4}+\frac{35}{11}:\frac{245}{121}=\frac{12.7}{7.4}+\frac{35}{11}.\frac{121}{245}=\frac{3.1}{1.1}+\frac{35}{11}.\frac{121}{245}=3+\frac{35}{11}.\frac{121}{245}=3+\frac{35.121}{11.245}=\frac{1.11}{1.7}=\frac{11}{7}\)

bạn làm giùm mình kết bài con lại nhá

=1/17

tam mai giải rõ cụ thể dc ko bn hii

\(A=\frac{7,2:2\times28,6+1,43\times2\times64}{1+3+5+7+...+49-339}\)

\(A=\frac{2\times3,6\times0,5\times1,43\times4\times5+1,43\times2\times0,5\times4\times32}{\left[\left(1+49\right)\times25:2\right]-339}\)

\(A=\frac{2\times0,5\times1,43\times4\times\left(3,6\times5+32\right)}{625-339}\)

\(A=\frac{5,72\times50}{286}\)

\(A=\frac{286}{286}\)

\(A=1\)

sorry mình bị lỗi!!!

a, 268

b,984

Bài 1: Tính

\(\text{1)}\) \(\dfrac{5}{8}.\dfrac{7}{30}-\dfrac{5}{2}.\dfrac{1}{8}\)

\(=\dfrac{5}{8}.\dfrac{7}{30}-\dfrac{5}{8}.\dfrac{1}{2}\)

\(=\dfrac{5}{8}.\left(\dfrac{7}{30}-\dfrac{1}{2}\right)\)

\(=\dfrac{5}{8}.\dfrac{-4}{15}\)

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

\(\text{2)}\) \(\dfrac{21}{10}.\dfrac{3}{4}-\dfrac{21}{10}-\dfrac{3}{4}\)

\(=\dfrac{63}{40}-\dfrac{21}{10}-\dfrac{3}{4}\)

\(=\dfrac{-21}{40}-\dfrac{3}{4}\)

\(=\dfrac{-51}{40}\)

\(\text{3)}\) \(\dfrac{-4}{11}:\dfrac{-6}{11}\)

\(=\dfrac{-4}{11}.\dfrac{11}{-6}\)

\(=\dfrac{4}{6}\)

\(\text{4)}\) \(\dfrac{2}{7}.\dfrac{14}{3}-1\)

\(=\dfrac{4}{3}-1\)

\(=\dfrac{1}{3}\)

\(\text{5)}\) \(\dfrac{4}{7}:\left(\dfrac{1}{5}.\dfrac{4}{7}\right)\)

\(=\dfrac{4}{7}:\dfrac{1}{5}:\dfrac{4}{7}\)

\(=1:\dfrac{1}{5}\)

\(=5\)

\(\text{6)}\) \(\dfrac{12}{7}.\dfrac{7}{4}+\dfrac{35}{11}:\dfrac{245}{121}\)

\(=3+\dfrac{35}{11}.\dfrac{121}{245}\)

\(=3+\dfrac{11}{7}\)

\(=3\dfrac{11}{7}=\dfrac{32}{7}\)

\(\text{7)}\) \(\left(\dfrac{4}{3}+\dfrac{8}{3}\right).\left(\dfrac{7}{4}-\dfrac{6}{4}\right):\left(\dfrac{6}{5}+\dfrac{12}{5}+\dfrac{1}{5}\right)\)

\(=4.\left(\dfrac{7}{4}-\dfrac{6}{4}\right):\left(\dfrac{6}{5}+\dfrac{12}{5}+\dfrac{1}{5}\right)\)

\(=4.\dfrac{1}{4}:\left(\dfrac{6}{5}+\dfrac{12}{5}+\dfrac{1}{5}\right)\)

\(=4.\dfrac{1}{4}:\dfrac{19}{5}\)

\(=1:\dfrac{19}{5}\)

\(=\dfrac{5}{19}\)

\(\text{8)}\) \(\left(\dfrac{1}{4}-\dfrac{1}{4}+\dfrac{\dfrac{1}{9}}{\dfrac{1}{9}}\right):\left(\dfrac{2}{3}+\dfrac{\dfrac{7}{15}}{\dfrac{2}{5}}-\dfrac{1}{6}\right)\)

\(=\left(0+1\right):\left(\dfrac{2}{3}+\dfrac{7}{15}:\dfrac{2}{5}-\dfrac{1}{6}\right)\)

\(=1:\left(\dfrac{2}{3}+\dfrac{7}{6}-\dfrac{1}{6}\right)\)

\(=1:\left(\dfrac{2}{3}+1\right)\)

\(=1:\dfrac{5}{3}\)

\(=\dfrac{3}{5}\)
\(\text{9)}\)

\(\left[\left(\dfrac{2}{193}-\dfrac{3}{389}\right).\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{1931}-\dfrac{11}{3862}\right).\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\left[\dfrac{199}{75077}.\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{1931}-\dfrac{11}{3862}\right).\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\left[\dfrac{199}{6613}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{1931}-\dfrac{11}{3862}\right).\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\dfrac{13235}{13226}:\left[\left(\dfrac{7}{1931}-\dfrac{11}{3862}\right).\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\dfrac{13235}{13226}:\left[\dfrac{3}{3862}.\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\dfrac{13235}{13226}:\left[\dfrac{3}{50}+\dfrac{9}{2}\right]\)

\(=\dfrac{13235}{13226}:\dfrac{114}{25}\)

\(=\dfrac{330875}{1507764}\)

a) \(2^n=8\)

\(\Rightarrow2^n=2^3\)

\(\Rightarrow n=3\)

b) \(5^{n+1}=125\)

\(\Rightarrow5^{n+1}=5^3\)

\(\Rightarrow n+1=3\)

\(\Rightarrow n=3-1=2\)

c) Mình không rõ đề:

d) \(2\cdot7^{n-1}+3=101\)

\(\Rightarrow2\cdot7^{n-1}=101-3\)

\(\Rightarrow2\cdot7^{n-1}=98\)

\(\Rightarrow7^{n-1}=\dfrac{98}{2}\)

\(\Rightarrow7^{n-1}=49\)

\(\Rightarrow7^{n-1}=7^2\)

\(\Rightarrow n-1=2\)

\(\Rightarrow n=1+2=3\)

e) \(3\cdot5^{2n+1}-6^2=339\)

\(\Rightarrow3\cdot5^{2n+1}=339+36\)

\(\Rightarrow3\cdot5^{2n+1}=375\)

\(\Rightarrow5^{2n+1}=125\)

\(\Rightarrow5^{2n+1}=5^3\)

\(\Rightarrow2n+1=3\)

\(\Rightarrow2n=2\)

\(\Rightarrow n=\dfrac{2}{2}=1\)