Đặt \(A=3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^9}\)
\(A=3.\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\right)\)
\(A=3.\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{256}-\frac{1}{512}\right)\)
\(A=3.\left(2-\frac{1}{512}\right)=3.\frac{1023}{512}=\frac{3069}{512}\)
Tính nhah ---- giúp mik giải nâ các bn thank nhiều nhiều
a)\(\frac{1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}}:\frac{3+\frac{3}{2}+\frac{3}{3}+\frac{3}{4}}{2-\frac{2}{2}+\frac{2}{3}-\frac{2}{4}}+\frac{1}{3}\)
b) \(\frac{\frac{1}{3}-\frac{1}{5}-\frac{1}{7}}{\frac{2}{3}-0,4-\frac{2}{7}}+\frac{\frac{3}{8}-\frac{3}{16}-\frac{3}{32}+\frac{3}{64}}{\frac{1}{4}-\frac{1}{8}-\frac{1}{16}+\frac{1}{32}}\)
c) \(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\)
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, \(B=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}\)
\((9-\frac{3}{5}+\frac{2}{3})-(7+\frac{7}{5}-\frac{3}{2})-(3-\frac{9}{5}+\frac{5}{2})\)
\(\frac{200-\left(3+\frac{2}{3}+\frac{2}{4}+\frac{2}{5}+.......+\frac{2}{100}\right)}{\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+......+\frac{9}{100}}\)
Chứng minh = 2
\(S=3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+....+\frac{3}{2^9}\)
Tính ?
A.\(3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^9}\)
B.\(\frac{4}{3.5}+\frac{4}{5.7}+\frac{4}{7.9}+...\frac{4}{2015.2017}\)
tính hợp lí
1, \(\frac{-17,5+\frac{5}{3}-2\frac{1}{7}}{7-\frac{2}{3}+\frac{6}{7}}\)
2, \(5,25+3\frac{4}{9}+2\frac{1}{27}+4,75+3\frac{1}{4}+2+\frac{3}{4}\)
3, \(12\frac{3}{5}+\frac{17}{24}+\frac{7}{5}\)
4, \(4\frac{2}{3}+2\frac{1}{5}+2\frac{2}{3}+3\frac{3}{5}\)
bài 1:
a)\(\frac{3}{10}.\left(\frac{-5}{9}+\frac{3}{5}\right)-\frac{3}{10}.\left(\frac{3}{9}_{ }-\frac{2}{5}\right)\)
b)\(\frac{-2}{5}.\left(\frac{5}{17}-\frac{9}{15}\right)-\frac{2}{5}.\left(\frac{2}{17}+\frac{-2}{5}\right)\)
MÌNH CẦN GẤP VÀO NGÀY 31/3/2018
1 CMR:
B=\(\frac{4}{3}+\frac{7}{3^2}+\frac{10}{3^3}+.....+\frac{3n+1}{3^n}< \frac{11}{4}\)(n thuộc N*;n>3)
A=\(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
C=\(\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+...+\frac{3^{20}-1}{3^{20}}>19\frac{1}{2}\)
