Chọn Câu trả lởi đúng
1.
\(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{204.205}=?\)
A. \(\dfrac{8}{41}\) B. \(\dfrac{43}{8}\)
C. \(\dfrac{1}{5}\) D. \(\dfrac{41}{8}\)
E. Tất cả ý trên đều sai
2.
\(\dfrac{\dfrac{5}{11}+\dfrac{5}{101}-\dfrac{5}{1979}}{\dfrac{3}{11}+\dfrac{3}{101}-\dfrac{3}{1979}}+\dfrac{\dfrac{2}{131}-\dfrac{2}{13}-\dfrac{2}{49}}{\dfrac{3}{131}+\dfrac{3}{13}+\dfrac{3}{49}}=?\)
A. \(1\) B. \(\dfrac{7}{3}\)
C. \(-1\) D. \(\dfrac{7}{6}\)
E. Tất cả ý trên đều sai
Chứng minh rằng: \(\dfrac{9}{10!}+\dfrac{9}{11!}+\dfrac{9}{12!}+...+\dfrac{9}{1000!}< \dfrac{1}{9!}\)
chứng minh rằng :
a) \(\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{4}\) b)\(\dfrac{1}{5^2}+\dfrac{1}{6^5}+...+\dfrac{1}{2013^2}+\dfrac{1}{2014}>\dfrac{1}{5}\)
Chứng minh rằng :
\(\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{2013^2}+\dfrac{1}{2014^2}>\dfrac{1}{5}\)
Chứng minh rằng : \(\dfrac{1}{16}+\dfrac{1}{36}+\dfrac{1}{64}+........+\dfrac{1}{2020^2}< \dfrac{1}{4}\)
chứng minh rằng :
\(\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{4}\)
Cho ba phân số bằng nhau \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\) . Chứng minh rằng : \(^{\left(\dfrac{a}{b}\right)^3}\)= \(\dfrac{a}{d}\)
Bài 1. Thực hiện phép tính:
a) |5.0,6+\(\dfrac{2}{3}\)|- \(\dfrac{1}{3}\)
b)(0,25 - 1\(\dfrac{1}{4}\)) : 5 - \(\dfrac{1}{5}\).(-3)\(^2\)
c)\(\dfrac{14}{17}.\dfrac{7}{5}-\dfrac{-3}{17}:\dfrac{5}{7}\)
d)\(\dfrac{7}{16}+\dfrac{-9}{25}+\dfrac{9}{16}+\dfrac{-16}{25}\)
e)\(\dfrac{5}{6}+2\sqrt{\dfrac{4}{9}}\)
Chứng minh rằng:
\(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}< \dfrac{3}{16}\)