=2/3+-1/6

=1/2 NHA

thank you Lê Hải Vân nha

\(x-\frac{1}{2}=\frac{3}{10}\times\frac{5}{6}\)

\(x-\frac{1}{2}=\frac{1}{4}\)

\(x=\frac{1}{4}+\frac{1}{2}\)

\(x=\frac{3}{4}\)

@muối

\(x-\dfrac{1}{2}=\dfrac{15}{60}=\dfrac{1}{4}\Leftrightarrow x=\dfrac{1}{4}+\dfrac{1}{2}=\dfrac{3}{4}\)

\(A=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2021}}\)

\(5A=1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2020}}\)

\(5A-A=\left(1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{2020}}\right)-\left(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{2021}}\right)\)

\(4A=1-\frac{1}{5^{2021}}< 1\)

Suy ra \(A< \frac{1}{4}\).

a)A=(\(\frac{1}{2}\)+1).(\(\frac{1}{3}\)+1)(\(\frac{1}{4}\)+1)...(\(\frac{1}{99}\)+1)

   A=\(\frac{3}{2}\).\(\frac{4}{3}\).\(\frac{5}{4}\)...\(\frac{100}{99}\)

   A=\(\frac{3.4.5...100}{2.3.4...99}\)

   A=\(\frac{100}{2}\)=50.

b) B=\(\frac{5^2}{1.6}\)+\(\frac{5^2}{6.11}\)+...+\(\frac{5^2}{46.51}\)

    B= 5(\(\frac{5}{1.6}\).\(\frac{5}{6.11}\)....\(\frac{5}{46.51}\))

    B= 5(  1-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{11}\)+...+\(\frac{1}{46}\)-\(\frac{1}{51}\) )

    B= 5.(1-\(\frac{1}{51}\)) \(\Rightarrow\)B= 5.\(\frac{50}{51}\)

    B= \(\frac{250}{51}\)

\(M=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\\ =1-\dfrac{1}{100}\\ =\dfrac{99}{100}\)

TL

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

=\(1-\frac{1}{100}\)

=\(\frac{100}{100}-\frac{1}{100}\)

=\(\frac{99}{100}\)

nha bn

HT

Ta có:

\(E=\frac{500^{40}+1}{500^{41}+1}\Leftrightarrow10E=\frac{500^{41}+10}{500^{41}+1}=1+\frac{9}{500^{41}+1}\)

\(W=\frac{500^{39}+1}{500^{40}+1}\Leftrightarrow10W=\frac{500^{40}+10}{500^{40}+1}=1+\frac{9}{500^{40}+1}\)

Hay ta đang so sánh: \(E=\frac{9}{500^{41}};W=\frac{9}{500^{40}}\)

Vì \(500^{41}>500^{40}\)nên \(\frac{9}{500^{41}}< \frac{9}{500^{40}}\)hay \(\frac{500^{40}+1}{500^{41}+1}< \frac{500^{39}+1}{500^{40}+1}\).

Vậy \(E< W\)

• chúc bạn thì tốt nhớ gửi cái này cho 20 người khác gửi đi nếu ko gửi điểm của bạn toàn là 1,2đ gửi tiếp đi đừng giữ cho riêng mình

\(\frac{35}{8}\cdot\left(-\frac{2}{21}\right):\left(-\frac{5}{24}\right)\)

\(=\left(-\frac{70}{168}\right):\left(-\frac{5}{24}\right)\)

\(=\left(-\frac{35}{84}\right):\left(-\frac{5}{24}\right)\)

\(=\left(-\frac{35}{84}\right)\cdot\left(-\frac{24}{5}\right)\)

\(=\frac{840}{420}\)

\(=\frac{1}{2}\)

Mong bn k, HT

=2 nhé HT

cho e loi giai chi tiet vs a