\(M=\dfrac{5^3}{1\cdot6}+\dfrac{5^3}{6\cdot11}+...+\dfrac{5^3}{26\cdot31}\)
\(=5^2\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{26\cdot31}\right)\)
\(=5^2\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
\(=5^2\left(1-\dfrac{1}{31}\right)\)\(=25\cdot\dfrac{30}{31}=\dfrac{750}{31}\)
[Bài này nhiều câu lắm, những 12 câu cơ, sợ các bạn thấy dài là nản! Tí nữa đăng tiếp! - 03/12 câu]
Tính tổng sau bằng phương pháp hợp lý nhất:
1) A = \(\dfrac{5^2}{1.6}\) + \(\dfrac{5^2}{6.11}\) + ... + \(\dfrac{5^2}{26.31}\)
2) B = \(\dfrac{6}{15.18}\) + \(\dfrac{6}{18.21}\) + \(\dfrac{6}{21.24}\) + ... + \(\dfrac{6}{87.90}\)
3) C = \(\dfrac{3^2}{8.11}\) + \(\dfrac{3^2}{11.14}\) + ... + \(\dfrac{3^2}{197.200}\)
Các bạn cố gắng giải đầy đủ giúp mình!
A=5^2/1.6+5^2/6.11+.....+5^2/26.31
Tính giá trị biểu thức sau:
P = \(\dfrac{3}{1.6}\)+\(\dfrac{3}{6.11}\)+\(\dfrac{3}{11.17}\)+...+\(\dfrac{3}{96.101}\)
1 Thực hiện phép tính:
A=\(\dfrac{1}{15.16}+\dfrac{1}{16.17}+...+\dfrac{1}{2016.2017}\)
B=\(\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{4}\right)+\left(1-\dfrac{1}{8}\right)+...+\left(1-\dfrac{1}{1024}\right)\)
C=\(\dfrac{1}{5.8}+\dfrac{1}{8.11}+...+\dfrac{1}{101.104}\)
D=\(\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+...+\dfrac{2}{101.104}\)
E=\(\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{101.106}\)
Chứng minh rằng:
1) B =\(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{19}>1\)
2) \(A=\dfrac{1}{5}+\dfrac{2}{5^2}+\dfrac{3}{5^3}+\dfrac{4}{5^4}+...+\dfrac{500}{5^{500}}<100\)
3) \(C=\dfrac{1}{2^3}+\dfrac{1}{3^3}+\dfrac{1}{4^3}+\dfrac{1}{5^3}+...+\dfrac{1}{500^3}<\dfrac{1}{4}\)
4) \(D=\dfrac{4}{3}+\dfrac{10}{9}+\dfrac{28}{27}+...+\dfrac{3^{98}+1}{3^{98}}<100\)
Làm giúp mình sớm nha! Thanks.
Cho \(S=\dfrac{10}{1.6}+\dfrac{10}{6.11}+...+\dfrac{10}{101.106}\)
Bài 1; Tính
a)\(\left(\dfrac{5}{18}-\dfrac{7}{24}+\dfrac{1}{9}\right):\dfrac{7}{18}\)
b)\(\left(\dfrac{7}{20}-\dfrac{5}{16}+\dfrac{3}{40}\right):\left(\dfrac{4}{15}-\dfrac{3}{10}+\dfrac{1}{12}\right)\)
Bài 2:Tìm x
a)\(\dfrac{3}{10}-x=\dfrac{5}{6}-\dfrac{2}{15}\)
b)\(\dfrac{-5}{8}+x=\dfrac{4}{9}-\dfrac{7}{1}\)
c)\(\dfrac{2}{x-3}=\dfrac{x-3}{18}\)
Giúp mk zới m.n mk gấp lắm mk tick cho
\(Tính: B = \dfrac{2 - \dfrac{2}{19} + \dfrac{2}{43} - \dfrac{2}{2017}}{3 - \dfrac{3}{19} + \dfrac{3}{43} - \dfrac{3}{2017}} :\dfrac{4 - \dfrac{4}{29} + \dfrac{4}{41} - \dfrac{4}{2018}}{5 - \dfrac{5}{29} + \dfrac{5}{41} - \dfrac{5}{2018}} \)
Câu 2: Tính ( theo BT của mình là các câu ko theo thứ tự nha )
i) 3\(\dfrac{1}{5}\) + 2\(\dfrac{2}{3}\) ;
k) 3\(\dfrac{1}{2}\) - 1\(\dfrac{2}{5}\) ;
l) 5\(\dfrac{1}{2}\). 3\(\dfrac{3}{4}\) ;
x) \(\dfrac{6}{11}\)-\(\dfrac{4}{11}\). \(\dfrac{22}{8}\) ;
m) 6\(\dfrac{1}{3}\):4\(\dfrac{2}{9}\) ;
r) (\(\dfrac{5}{7}\)-\(\dfrac{1}{2}\)) : \(\dfrac{3}{5}\)
s) \(\dfrac{6}{7}\) + \(\dfrac{4}{7}\). \(\dfrac{7}{8}\)
=> GIúp mình nhanh nha - ai đúng; nhanh; trình bày đẹp thì mình TICK !
