ta có: \(B=\frac{2}{3}+\frac{2}{3^2}+\frac{2}{3^3}+...+\frac{2}{3^{1000}}\)
\(\Rightarrow3B=2+\frac{2}{3}+\frac{2}{3^2}+...+\frac{2}{3^{999}}\)
\(\Rightarrow3B-B=2-\frac{2}{3^{1000}}\)
\(2B=2-\frac{2}{3^{1000}}\)
\(B=\frac{2-\frac{2}{3^{1000}}}{2}\)
Thu gọn:
\(B=\frac{\frac{1}{2}-\frac{1}{2}:\frac{3}{4}-\frac{3}{4}}{\frac{2}{3}-\frac{2}{3}:\frac{5}{6}-\frac{5}{6}}\)
Thu gọn
\(B=\frac{2^3-3^4-2^4.3^3}{2^5.3^4-2^6.3^3}\)
\(C=\frac{\frac{1}{2}-\frac{1}{2}:\frac{3}{4}-\frac{3}{4}}{\frac{2}{3}-\frac{2}{3}:\frac{5}{6}-\frac{5}{6}}\)
Thu gọn tổng sau:
A= \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}\)
Rút gọn
\(\frac{3-\frac{1}{5}+\frac{3}{20}}{2+\frac{1}{4}-\frac{3}{5}}\)
Tính
a/ \(\frac{3}{4}.\frac{8}{9}.\frac{15}{10}....\frac{9999}{1000}\)
b/ \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}< 1\)
Rút gọn :
a/ \(A=\frac{\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+...+\frac{19}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}}\)
b/ \(B=\frac{\left(1+\frac{2012}{1}\right)\left(1+\frac{2012}{2}\right)...\left(1+\frac{2012}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)...\left(1+\frac{1000}{2012}\right)}\)
Rút gọn các tổng sau:
\(A=\frac{1}{2}+\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+\left(\frac{1}{2}\right)^4+...+\left(\frac{1}{2}\right)^{2015}\)
\(B=1+\frac{1}{3}+\left(\frac{1}{3}\right)^2+\left(\frac{1}{3}\right)^3+...+\left(\frac{1}{3}\right)^{2016}\)
1.tính
\(\frac{2}{3}+\frac{1}{3}\)
\(\frac{3}{4}+\frac{2}{4}+\frac{1}{4}\)
\(\frac{4}{5}+\frac{3}{5}+\frac{2}{5}+\frac{1}{5}\)
\(\frac{5}{6}+\frac{4}{6}+\frac{3}{6}+\frac{2}{6}+\frac{1}{6}\)
Từ các phép tính trên ,hãy tính giá trị tổng dưới đây
\(\frac{999}{1000}+\frac{998}{1000}+\frac{997}{1000}+...+\frac{1}{1000}\)
cách olamf lun nah các bn
Rút gọn tổng sau:
\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{10}}\)
Rút gọn:
\(A=\frac{\frac{2}{7}+\frac{2}{5}+\frac{2}{17}-\frac{2}{293}}{\frac{3}{7}+\frac{3}{5}+\frac{3}{17}+\frac{3}{293}}\)
