N=\(1+2+2^2+2^3+...+2^{299}+2^{300}\)

N=\(\left(1+2+2^2\right)+\left(2^3+2^4+2^5\right)+...+\left(2^{297}+2^{298}+2^{299}\right)+2^{300}\)

N=\(7+2^3\left(1+2+2^2\right)+2^6\left(1+2+2^2\right)+...+2^{297}\left(1+2+2^2\right)+2^{300}\)

N=\(7+2^3.7+2^6.7+...+2^{297}.7+2^{300}\)

N=\(7.\left(1+2^3+2^6+...+2^{297}\right)+2^{300}\)

Ta thấy ​\(7.\left(1+2^3+2^6+...+2^{297}\right)⋮7\)​

Còn lại ta xét số \(2^{300}\).

Khi phân tích ra thừa số nguyên tố thì số \(2^{300}\)không chứa thừa số 7.\(\Rightarrow2^{300}\)không chia hết cho 7

Vậy N không chia hết cho 7.

Đặt A=\(1-2+2^2-2^3+2^4-...+2^{1000}\)

A.2=​\(2.\left(1-2+2^2-2^3+2^4-...+2^{1000}\right)\)​

A.2=\(2-2^2+2^3-2^4+...+2^{1001}\)

A.2+A=\(\left(2-2^2+2^3-2^4+...+2^{1001}\right)+\left(1-2+2^2-2^3+...+2^{1000}\right)\)

A=\(\dfrac{2}{7}+\dfrac{-3}{8}+\dfrac{11}{7}+\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{5}{-3}\)

A=\(\left(\dfrac{2}{7}+\dfrac{11}{7}+\dfrac{1}{7}\right)+\left(\dfrac{1}{3}+\dfrac{5}{-3}\right)+\dfrac{-3}{8}\)

A=\(2+\dfrac{-4}{3}+\dfrac{-3}{8}\)

A=\(\dfrac{7}{24}\)

B=\(\left(\dfrac{3}{17}+\dfrac{14}{17}\right)+\left(\dfrac{-18}{35}+\dfrac{17}{-35}\right)+\left(\dfrac{-5}{13}+\dfrac{-8}{13}\right)\)

B=\(\dfrac{17}{17}+\dfrac{-35}{35}+\dfrac{-13}{13}\)

B=\(1+\left(-1\right)+\left(-1\right)=-1\)

C=\(\dfrac{-3}{17}+\left(\dfrac{2}{3}+\dfrac{3}{17}\right)\)

C=\(\dfrac{-3}{17}+\dfrac{2}{3}+\dfrac{3}{17}=\left(\dfrac{-3}{17}+\dfrac{3}{17}\right)+\dfrac{2}{3}\)

C=0+\(\dfrac{2}{3}=\dfrac{2}{3}\)

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

D=\(\dfrac{-1}{6}+\dfrac{5}{-12}+\dfrac{7}{12}\)

D=\(\dfrac{-2}{12}+\dfrac{-5}{12}+\dfrac{7}{12}=\left(\dfrac{-2}{12}+\dfrac{-5}{12}\right)+\dfrac{7}{12}\)

D=\(\dfrac{-7}{12}+\dfrac{7}{12}=0\)

A=1-\(\dfrac{4}{5.7}-\dfrac{4}{7.9}-\dfrac{4}{9.11}...-\dfrac{4}{59.61}\)

A=\(1-\left(\dfrac{4}{5.7}+\dfrac{4}{7.9}+\dfrac{4}{9.11}+...+\dfrac{4}{59.61}\right)\)

Đặt B=​\(\dfrac{4}{5.7}+\dfrac{4}{7.9}+\dfrac{4}{9.11}+...+\dfrac{4}{59.61}\)​

23.(42 - x) = 19.x

23.42 - 23x = 19x

23x + 19x = - 23.42

42x = (-23).42

\(\Rightarrow\) x = - 23

Câu 1:

a,\(x=\dfrac{1}{4}+\dfrac{2}{13}\)

\(x=\dfrac{13}{52}+\dfrac{8}{52}=\dfrac{21}{52}\)

Câu 2:

a,\(\dfrac{-2}{5}+\dfrac{3}{-4}+\dfrac{6}{7}+\dfrac{3}{4}+\dfrac{2}{5}\)

\(=\left(\dfrac{-2}{5}+\dfrac{2}{5}\right)+\left(\dfrac{3}{-4}+\dfrac{3}{4}\right)+\dfrac{6}{7}\)

=\(0+0+\dfrac{6}{7}=\dfrac{6}{7}\)

b,\(\dfrac{7}{15}+\dfrac{4}{-9}+\dfrac{-2}{11}+\dfrac{8}{15}+\dfrac{-5}{9}\)

=\(\left(\dfrac{7}{15}+\dfrac{8}{15}\right)+\left(\dfrac{4}{-9}+\dfrac{-5}{9}\right)+\dfrac{-2}{11}\)

=\(\dfrac{15}{15}+\dfrac{-9}{9}+\dfrac{-2}{11}=1+\left(-1\right)+\dfrac{-2}{11}\)

=\(0+\dfrac{-2}{11}=\dfrac{-2}{11}\)

c, \(\dfrac{-5}{7}+\dfrac{5}{13}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-21}{41}\)

=\(\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(\dfrac{-20}{41}+\dfrac{-21}{41}\right)+\dfrac{-5}{7}\)

=\(\dfrac{13}{13}+\dfrac{-41}{41}+\dfrac{-5}{7}=1+\left(-1\right)+\dfrac{-5}{7}\)

=\(0+\dfrac{-5}{7}=\dfrac{-5}{7}\)

Đề bài câu b bài 1 là gì vậy bạn?

Bài 1:

A=\(\dfrac{\dfrac{5}{12}+\dfrac{3}{4}-1}{3-\dfrac{5}{6}+\dfrac{2}{3}}+\dfrac{\dfrac{16}{5}+\dfrac{16}{7}-\dfrac{16}{9}}{\dfrac{17}{5}+\dfrac{17}{7}-\dfrac{17}{9}}\)

A=\(\dfrac{\dfrac{1}{6}}{\dfrac{17}{6}}+\dfrac{16\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}\right)}{17\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}\right)}\)

A=\(\dfrac{1.\dfrac{1}{6}}{17.\dfrac{1}{6}}+\dfrac{16}{17}\)

A=\(\dfrac{1}{17}+\dfrac{16}{17}=\dfrac{17}{17}=1\)

Bài 2 mk chưa có câu trả lời, sorry nha!