Chứng tỏ rằng :\(\dfrac{1}{101}+\dfrac{1}{102}+...+\dfrac{1}{299}+\dfrac{1}{300}>\dfrac{2}{3}\)
Tính tích \(A=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}...\dfrac{899}{900}\)
Chứng tỏ rằng : \(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{17}< 2\)
Tính giá trị của biểu thức sau :
\(M=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{10.11.12}\)
Cho \(A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+..............+\dfrac{1}{18.19.20}\) Chứng minh \(A< \dfrac{1}{4}\)
Help me!!!!!!!
E =\(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{98.99.100}\)
\(B=\dfrac{1}{1.2.3}+\dfrac{1}{3.4.5}+.........+\dfrac{1}{n.\left(n+1\right).\left(n+2\right)}\)
Tìm số tự nhiên x biết :
\(\left(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{8.9.10}\right).x=\dfrac{23}{45}\)
Bài 1: Cho A=\(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)
a) Chứng minh: A=\(\dfrac{1}{51}+\dfrac{1}{52}+\dfrac{1}{53}+...+\dfrac{1}{100}\)
b) Chứng minh: A<\(\dfrac{5}{6}\)
Bài 1:
a, Cho A = \(\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+....+\dfrac{1}{100^2}\)
Chứng tỏ: A <\(\dfrac{1}{2}\)
b, Cho B = \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+....+\dfrac{1}{2^{20}}\)
Chứng tỏ B < 1
c, Cho C = \(\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}\)
Chứng tỏ C < \(\dfrac{1}{2}\)
d, Cho D = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{20^2}\)
Chứng tỏ D < 1
\(\dfrac{1}{51}+\dfrac{1}{52}+\dfrac{1}{53}+...+\dfrac{1}{100}:\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\)
1) Tìm 2 số nguyên tố x, y sao cho: \(x^2-6y^2=1\)
2) Cho \(B=1.2.3...2012.\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}\right)\)
CMR: B chia hết cho 2013
