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-1( 1+1/2+1/4+1/8+...+1/1024)
= -1.( 1+ 1-1/2+1/2-1/4+1/4-1/8+...+1/512-1/1024)
= -1.( 1+ 1-1/1024)
=-( 2- 1/1024)
= - 2047/ 1024
p/s : mk chỉ nghĩ ra cách lm thui, chớ về phần tính toán mk sợ sai, nếu sai mong bạn thông cảm nha! ( mk nghĩ kq sai !)
1) tự làm (thực hiện từ dưới lên)
2) B = \(\frac{\left(\frac{1}{2}\right)^{10}.5-\left(\frac{1}{4}\right)^5.3}{\frac{\frac{1}{1024}.1}{3}-\left(\frac{1}{2}\right)^{11}}\)
= \(\frac{\left(\frac{1}{2}\right)^{10}.5-\left(\frac{1}{2}\right)^{10}.3}{\left(\frac{1}{2}\right)^{10}.\frac{1}{3}-\left(\frac{1}{2}\right)^{10}.\frac{1}{2}}\)
= \(\frac{\left(\frac{1}{2}\right)^{10}.\left(5-3\right)}{\left(\frac{1}{2}\right)^{10}.\left(\frac{1}{3}-\frac{1}{2}\right)}\)
= \(\frac{2}{-\frac{1}{6}}\)= 2 . (-6) = -12
1) \(5+\frac{1}{1+\frac{1}{1+\frac{2}{1+\frac{3}{4}}}}=5+\frac{15}{7}=\frac{5}{1}+\frac{15}{7}=\frac{50}{7}\)
Cách 1:
\(\left(6-\frac{2}{3}+\frac{1}{2}\right)-\left(5+\frac{5}{3}-\frac{3}{2}\right)-\left(3-\frac{7}{3}+\frac{5}{2}\right)\)
=\(\frac{35}{6}-\frac{31}{6}-\frac{19}{6}\)
=\(\frac{35-31-19}{6}\)
=\(-\frac{15}{6}=-\frac{5}{2}\)
Cách 2:
\(\left(6-\frac{2}{3}+\frac{1}{2}\right)-\left(5+\frac{5}{3}-\frac{3}{2}\right)-\left(3-\frac{7}{3}+\frac{5}{2}\right)\)
=\(6-\frac{2}{3}+\frac{1}{2}-5-\frac{5}{3}+\frac{3}{2}-3+\frac{7}{3}-\frac{5}{2}\)
=\(\left(-\frac{2}{3}-\frac{5}{3}+\frac{7}{3}\right)+\left(\frac{1}{2}+\frac{3}{2}-\frac{5}{2}\right)+\left(6-5-3\right)\)
=\(0-\frac{1}{2}-2\)
=\(-\frac{5}{2}\)
đặt A = \(-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{1024}\)
ta có:
A = \(-1-\frac{1}{2}-\frac{1}{4}-...-\frac{1}{1024}\)
A = \(-\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\right)\)
Đặt B = \(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\)
ta có:
B = \(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\)
=> 2B = \(2+1+\frac{1}{2}+...+\frac{1}{512}\)
=> 2B - B = \(\left(2+1+\frac{1}{2}+...+\frac{1}{512}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\right)\)
=> B = \(2-\frac{1}{1024}\)
=> B = \(\frac{2048}{1024}-\frac{1}{1024}=\frac{2047}{1024}\)
Thay B vào A ta có:
A = \(\frac{-2047}{1024}\)
vậy A = \(\frac{-2047}{1024}\)
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