Violympic toán 7
Các câu hỏi tương tự
Thực hiện phép tính :
\(D=\frac{2.2018}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+2018}}\)
Tính P = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2019}}{\frac{2018}{1}+\frac{2017}{2}+\frac{2016}{3}+....\frac{1}{2018}}\)
Cho S = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\)
P = \(1+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2018}\)
Chứng minh rằng: \(\left(S-P\right)^{2018}=1\)
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...-\frac{1}{2016}+\frac{1}{2017}-\frac{1}{2018}\)
\(B=\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\)
Tính \(\left(A^{2017}-B^{2017}\right)^{2018}\)
Tính tổng sau
1) B= 1.2+2.3+3.4+......+99.100
2) C= \(1^2+2^2+3^2+...+99^2\)
3) D= \(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right).....\left(1-\frac{1}{n^2}\right)\)
4) E=\(\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+....+\frac{1}{3^{100}}\)
Tính bằng cách hợp lí
a)\(\frac{1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}}:\frac{13+\frac{13}{2}+\frac{13}{3}+\frac{13}{4}}{17-\frac{17}{2}+\frac{17}{3}-\frac{17}{4}}\)
b)\(\frac{0,125-\frac{1}{5}+\frac{1}{7}}{0,375-\frac{3}{5}+\frac{3}{7}}+\frac{\frac{1}{2}+\frac{1}{3}-0,2}{\frac{3}{4}+0,5-\frac{3}{10}}\)
B1 : Tìm GTNN :
\(\left(x+2020\right)^4+\left|y-2019\right|-2018\)
B2 : Tính :
\(P=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+\frac{1}{4}.\left(1+2+3+4\right)+...+\frac{1}{2019}.\left(1+2+3+...+2019\right)\)
bài 1: tính A:=\(\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}+\frac{5}{6}-\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{2}{3}-\frac{1}{2}\)
Bài 2: Cho B=\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+.....+\frac{1}{49}-\frac{1}{50}\)
Chứng minh rằng: \(\frac{7}{12}< A< \frac{5}{6}\)
1.Tính :
\(\left(1\frac{1}{1+2}\right).\left(1\frac{1}{1+2+3}\right)...\left(1\frac{1}{1+2+3+...+2018}\right)\)