chứng minh rằng \(\frac{1}{65}\)<\(\frac{1}{5^3}+\frac{1}{6^3}+...+\frac{1}{2004^3}\)<\(\frac{1}{40}\)

Chứng minh rằng:

\(\frac{1}{65}\)<\(\frac{1}{5^3}\)+\(\frac{1}{6^3}\)+\(\frac{1}{7^3}\)+...+\(\frac{1}{2004^3}\)<\(\frac{1}{40}\)

Bài 4 :

a) Tính giá trị của biểu thức :

\(A=\left(\frac{1\frac{11}{31}\cdot4\frac{3}{7}-\left(15-6\frac{1}{3}\cdot\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-5\frac{1}{3}\right)}\cdot\left(-1\frac{14}{93}\right)\right)\cdot\frac{31}{50}\)

b) Chứng tỏ rằng : \(B=1-\frac{1}{2^2}-\frac{1}{3^2}-\frac{1}{3^2}-...-\frac{1}{2004^2}>\frac{1}{2004}\)

Chứng minh rằng: \(\frac{1}{5^3}+\frac{1}{6^3}+\frac{1}{7^3}+...+\frac{1}{2013^3}< \frac{1}{40}\)

Chứng minh rằng \(\frac{1}{5^3}+\frac{1}{6^3}+\frac{1}{7^3}+....+\frac{1}{2013^3}<\frac{1}{40}\)

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: \(\frac{7}{12}< A< \frac{5}{6}\)

chứng minh rằng

\(1< \frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+...+\frac{1}{3n+1}< 2\)

\(\frac{3}{5}< \frac{1}{2004}+\frac{2}{2005}+\frac{2}{2006}+...+\frac{1}{4006}< \frac{3}{4}\)

BÀI 1:TÍNH:

\(B=1+\frac{3}{2^3}+\frac{4}{2^4}+\frac{5}{2^5}+....+\frac{100}{2^{100}}\)

BÀI 2: CHỨNG MINH RẰNG:

\(B=1-\frac{1}{2^2}-\frac{1}{3^2}-.....-\frac{1}{2004^2}>\frac{1}{2004}\)

BÀI 3:THỰC HIỆN PHÉP TÍNH BẰNG CÁCH HỢP LÝ:

\(B=\frac{1}{3}+\frac{1}{6}.\left(1+2\right)+\frac{1}{9}.\left(1+2+3\right)+.....+\frac{1}{6045}.\left(1+2+3+....+2015\right)\)

chứng minh rằng :\(\frac{1}{4}+\frac{2}{4^2}+\frac{3}{4^3}+\frac{4}{4^4}+.........+\frac{2004}{4^{2004}}