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Quy luật của dãy :
\(\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{5}\right)=\frac{1}{2^2}\cdot\frac{1}{5}=\frac{1}{4}\cdot\frac{1}{5}=\frac{1}{20}\)
\(\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{5}\right)\left(\frac{1}{2}-\frac{1}{7}\right)=\frac{1}{2^3}\cdot\frac{1}{7}=\frac{1}{56}\)
Tương tự : Vì dãy có :
(99 - 3) : 2 + 1 = 49 (số hạng)
\(\Rightarrow T=\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{3}\right)...\left(\frac{1}{2}-\frac{1}{99}\right)\)
\(T=\frac{1}{2^{49}}\cdot\frac{1}{99}\)
a) \(=\frac{3}{2}.\frac{4}{3}....\frac{100}{99}=\frac{100}{2}=50\)
a) =3/2 . 4/3 . 5/4 ...100/99
=\(\frac{3.4.5...100}{2.3.4..99}\)
=\(\frac{100}{2}\)
b) =
1.
a.\(\left(\frac{1}{2}\right)^2=\frac{1}{4}\)
b. \(\left(\frac{1}{2}\right)^3=\frac{1}{8}\)
c. \(\left(\frac{-3}{5}\right)^5=\frac{-243}{3125}\)
d. \(\left(\frac{-1}{5}\right)^2=\frac{1}{25}\)
e. \(\left(\frac{-1}{6}\right)^3=\frac{-1}{216}\)
Trả lời:
Bài 1:
a, \(\left(\frac{1}{2}\right)^4=\frac{1^4}{2^4}=\frac{1}{16}\)
b, \(\left(\frac{1}{2}\right)^3=\frac{1^3}{2^3}=\frac{1}{8}\)
c, \(\left(\frac{-3}{5}\right)^2=\frac{\left(-3\right)^2}{5^2}=\frac{9}{25}\)
d, \(\left(\frac{-1}{5}\right)^2=\frac{\left(-1\right)^2}{5^2}=\frac{1}{25}\)
e, \(\left(\frac{-1}{6}\right)^3=\frac{\left(-1\right)^3}{6^3}=\frac{-1}{216}\)
Bài 2:
a, \(\left(\frac{3}{2}\right)^2.\left(\frac{4}{3}\right)^2=\frac{9}{4}.\frac{16}{9}=4\)
b, \(\left(-\frac{1}{2}\right)^3.\left(\frac{2}{3}\right)^3=-\frac{1}{8}.\frac{8}{27}=-\frac{1}{27}\)
c, \(\left(-\frac{1}{2}\right)^2.\left(\frac{2}{5}\right)^2=\frac{1}{4}.\frac{4}{25}=\frac{1}{25}\)
d, \(\left(-\frac{1}{2}\right)^3.\left(\frac{2}{3}\right)^3=-\frac{1}{8}.\frac{8}{27}=-\frac{1}{27}\)
e, \(\left(-5\right)^3.\frac{1}{5}=-125.\frac{1}{5}=-25\)
f, \(\left(\frac{2}{9}\right)^5.\left(-\frac{27}{4}\right)^5=\frac{2^5}{9^5}.\frac{\left(-27\right)^5}{4^5}=\frac{2^5.\left(-27\right)^5}{9^5.4^5}=\frac{2^5.\left[\left(-3\right)^3\right]^5}{\left(3^2\right)^5.\left(2^2\right)^5}=-\frac{2^5.3^{15}}{3^{10}.2^{10}}=\frac{3^5}{2^5}\)
\(\Rightarrow\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}=\frac{1}{5}\)
TINH LAN LUOT NHE