a\(\): \(K=1-5+5^2-5^3+...+5^{100}\)

=>\(5K=5-5^2+5^3-5^4+...+5^{101}\)

=>\(5K+K=5-5^2+5^3-5^4+...+5^{101}+1-5+5^2-5^3+...+5^{100}\)

=>\(6K=5^{101}+1\)

=>\(K=\dfrac{5^{101}+1}{6}\)

b: \(5^{101}\) chia 6 sẽ dư 5 bởi vì \(5^{101}+1⋮6\) và 1+5=6

Tan.has lunch at twenty to twelve

Tan has lunch at twenty to twelve

\(A=\dfrac{1}{2\cdot6}+\dfrac{1}{3\cdot8}+...+\dfrac{1}{2023\cdot4048}\)

\(=\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+...+\dfrac{2}{4046\cdot4048}\)

\(=\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{4046}-\dfrac{1}{4048}\)

\(=\dfrac{1}{4}-\dfrac{1}{4048}=\dfrac{1012-1}{4048}=\dfrac{1011}{4048}\)

\(A=\dfrac{1}{2\cdot6}+\dfrac{1}{3\cdot8}+\dfrac{1}{4\cdot10}+...+\dfrac{1}{2023\cdot4048}\)

\(=\dfrac{1}{2}\cdot\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{2023\cdot2024}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2023}-\dfrac{1}{2024}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{2024}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{1012-1}{2024}\)

\(=\dfrac{1011}{4048}\)

Có đáp án luôn rồi!

@456 troll thật

\(\left\{47-\left[736:\left(5-3\right)^4\right]\right\}.2021\)

\(=\left\{47-\left[736:2^4\right]\right\}.2021\)

\(=\left\{47-\left[736:16\right]\right\}.2021\)

\(=\left\{47-46\right\}.2021\)

\(=1.2021\)

\(=2021\)

\(\left\{47-\left[736:\left(5-3\right)^4\right]\right\}\cdot2021\)

\(=\left\{47-736:16\right\}\cdot2021\)

\(=\left(47-46\right)\cdot2021=2021\)

2(x-1)+3(x-2)=x-4

=> 2x-2+3x-6=x-4

=> 5x-8=x-4

=> 5x-x=8-4

=> 4x=4

=> x=4:4

=> x=1

Vậy: x=1

\(2\left(x-1\right)+3\left(x-2\right)=x-4\)

\(2x-2+3x-6=x-4\)

\(\left(2x+3x\right)-\left(2+6\right)=x-4\)

\(5x-8=x-4\)

\(5x-x=-4+8\)

\(4x=4\)

\(x=1\)

\(\left(2345-45\right)+2345\)

\(=2300+2345\)

\(=4645\)

\(\left(2345-45\right)+2345\)

\(=2300+2345\)

\(=4645\)

\(\left(7+x\right)-\left(21-13\right)=32\)

\(\left(7+x\right)-8=32\)

\(7+x=32+8\)

\(7+x=40\)

\(x=40-7\)

\(x=33\)

Vậy \(x=33\)

\(\left(7+x\right)-\left(21-13\right)=32\)

\(7+x-21+13=32\)

\(x+\left(7+13-21\right)=32\)

\(x-1=32\)

\(x=33\)

\(-11-\left(19-x\right)=50\)

\(-11-19+x=50\)

\(x-\left(11+19\right)=50\)

\(x-30=50\)

\(x=50+30\)

\(x=80\)

\(-11-\left(19-x\right)=50\Leftrightarrow19-x=-11-50=-61\Leftrightarrow x=19+61=80\)

= -1+ ( -1 ) + ( -1 ) + ( -1 ) + ( -1 ) 

= -2 + ( -3)

= - 5

chúc bạn học tốt

\(\text{11-12+13-14+15-16+17-18+19-20}\)

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

\(=\left(-1\right).5\)

\(=-5\)