\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
=> \(S=3\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)
Đặt \(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
=> \(2A=2+1+\frac{1}{2}+\frac{1}{2^8}\)
=> \(A=2A-A=2-\frac{1}{2^9}\)
=> \(S=3A=3\left(2-\frac{1}{2^9}\right)=6-\frac{3}{2^9}\)
Bài 1: Thực hiện phép tính(tính nhanh nếu có thể)
a) \(\frac{-4}{5}:\frac{8}{7}\)
b) \(\frac{-3}{8}.\frac{7}{9}+\frac{-3}{8}.\frac{2}{9}+0,25\)
c) 15\(\frac{3}{7}-\left(2\frac{4}{9}+11\frac{3}{7}\right)\)
Bài 2: Tìm x, biết:
a) x+\(\frac{2}{3}=\frac{5}{6}\)
b) 2\(\frac{3}{5}-8x=\left(\frac{1}{7}-\frac{1}{8}\right).56\)
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:
\(B=\frac{1}{3}+\frac{1}{6}.\left(1+2\right)+\frac{1}{9}.\left(1+2+3\right)+.....+\frac{1}{6045}.\left(1+2+3+....+2015\right)\)
Bài 3 : Tính:
a, A = \(\frac{2}{5}+\frac{-1}{6}-\frac{3}{4}-\frac{-2}{3}\)
b, B = \(\frac{7}{10}-\frac{-3}{4}+\frac{-5}{6}-\frac{1}{5}+\frac{-2}{3}\)
c, C = \(\frac{\left(\frac{1}{2}-0,75\right)\times\left(0,2-\frac{2}{5}\right)}{\frac{5}{9}-1\frac{1}{12}}\)
d, D = \(\frac{\frac{2}{3}+\frac{2}{7}-\frac{1}{4}}{-1-\frac{3}{7}+\frac{3}{28}}\)
Bài 1 : Tính
a) A = \(\frac{\frac{1}{12}-\frac{2}{9}-1}{\frac{5}{18}-\frac{-3}{4}-\frac{1}{9}}\)
Bài 2 : Tính
a) A = \(\frac{3-\frac{1}{2}+\frac{1}{4}}{\frac{2}{3}-\frac{5}{6}+\frac{-3}{4}}\) b) B = \(\frac{8-\frac{8}{5}+\frac{8}{25}-\frac{8}{125}}{9-\frac{9}{5}+\frac{9}{25}-\frac{9}{125}}\): \(\frac{161616}{151515}\)
Bài 2: (3 đ) Thực hiện phép tính
a)\(\left[4\frac{1}{9}+3\frac{1}{4}\right].2\frac{1}{4}+2\frac{3}{4}\)
b)\(1+\left[\frac{9}{10}-\frac{4}{5}\right]:3\frac{1}{6}\)
c)(-7+l13l)-(13-l-7l-25)-(25+l-10l-9)
Bài 2: (3 đ) Thực hiện phép tính:
a)\(\left[4\frac{1}{9}+3\frac{1}{4}\right].2\frac{1}{4}+2\frac{3}{4}\)
b)\(1+\left[\frac{9}{4}+\frac{4}{5}\right]:3\frac{1}{6}\)
c)(-7+|13|)-(13-|-7|-25)-(25+|-10|-9)
Bài 3 , Thực hiện phép tính :
a, \(A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}+\frac{3}{11}+\frac{3}{1001}+\frac{3}{13}}{\frac{9}{1001}+\frac{9}{13}+\frac{9}{7}+\frac{9}{11}+9}\)
b, \(B=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}\)
Bài 1 : Tính
a) A = \(\frac{\frac{1}{12}-\frac{2}{9}-1}{\frac{5}{18}+\frac{-3}{4}-\frac{1}{9}}\)
Bài 2 : Tính
a) A = \(\frac{3-\frac{1}{2}+\frac{1}{4}}{\frac{2}{3}-\frac{5}{6}+\frac{-3}{4}}\) b) B = \(\frac{8-\frac{8}{5}+\frac{8}{25}-\frac{8}{125}}{9-\frac{9}{5}+\frac{9}{25}-\frac{9}{125}}\): \(\frac{161616}{151515}\)
Bài 1: So Sánh phân số
a) \(\frac{5}{24}và\frac{5+10}{24}\) b) \(\frac{4}{9};\frac{6+9}{6.9};\frac{2}{3}\)
BÀI 2: Thực hiện phép tính
\(\left(-2\right)+\frac{-5}{8}\)
Bài 3: Tính
\(\frac{1}{2}+\frac{-1}{3}+\frac{1}{4}+\frac{-1}{5}+\frac{1}{6}+\frac{-1}{7}+\frac{1}{8}+\frac{1}{7}+\frac{-1}{6}+\frac{1}{5}+\frac{-1}{4}+\frac{1}{3}+\frac{-1}{2}\)
Bài 4: Tìm x
a) \(x=\frac{1}{6}+\frac{2}{5}\) b) \(\frac{x}{3}=\frac{2}{3}+\frac{-1}{7}\)
Bài 5: Cho \(A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\) so sánh A và \(\frac{1}{2}\)
Bài 6:
\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{101}{100}\)