Cho A = \(\)\(\frac{n+2}{n-3}\overset{}{}\) ( n ∈ Z )
a, Tìm n để A là phân số
b, Tìm n để A nhận giá trị nguyên
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A = \(\frac{9^{14}\times25^5\times8^7}{18^{12}\times625^2\times24^3}\)
A = \(\frac{\left(3^2\right)^{14}\times\left(5^2\right)^5\times\left(2^3\right)7}{\left(2.3^2\right)^{12}\times\left(5^4\right)^3\times\left(2^3.3\right)^3}\)
A = \(\frac{3^{28}\times5^{10}\times2^{21}}{2^{12}\times3^{24}\times5^{12}\times2^9\times3^3}\)
A = \(\frac{3^{28}\times5^{10}\times2^{21}}{\left(3^{24}.3^3\right)\times5^{12}\times\left(2^{12}\times2^9\right)}\)
A = \(\frac{3^{28}\times5^{10}\times2^{21}}{3^{27}\times5^{12}\times2^{21}}\)
A = \(\frac{3}{5^2}\)
A = \(\frac{3}{25}\)
\(\dfrac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}\)
\(=\dfrac{3^{28}\cdot5^{10}\cdot2^{21}}{\left(2\cdot3^2\right)^{12}\cdot\left(5^4\right)^3\cdot\left(2^3\cdot3\right)^3}\)
\(=\dfrac{2^{21}\cdot3^{28}\cdot5^{10}}{2^{12}\cdot3^{24}\cdot5^{12}\cdot2^9\cdot3^3}\)
\(=\dfrac{2^{21}}{2^{21}}\cdot\dfrac{3^{28}}{3^{27}}\cdot\dfrac{5^{10}}{5^{12}}=\dfrac{3}{5^2}=\dfrac{3}{25}\)
\(\frac{-5}{8}\) \(-\) \(\frac{7}{-12}\)
=\(\frac{-5}{8}-\frac{-7}{12}\) =\(\frac{-30}{48}-\frac{-28}{48}\)
=\(\frac{-2}{48}=\frac{-1}{24}\)
Tính:
\(-\frac58\) - \(\frac{7}{-12}\)
= \(-\frac{15}{24}\) + \(\frac{14}{24}\)
= - \(\frac{1}{24}\)
`-2/5 x + 4/3 = 3/5`
`=> -2/5 x = 3/5 - 4/3`
`=> -2/5 x = -11/15`
`=> x = -11/15 : -2/5`
`=> x = 11/6`
Vậy `x = 11/6`
Ta có: \(-\dfrac{2}{5}x+\dfrac{4}{3}=\dfrac{3}{5}\)
=>\(-\dfrac{2}{5}x=\dfrac{3}{5}-\dfrac{4}{3}=\dfrac{9}{15}-\dfrac{20}{15}=-\dfrac{11}{15}\)
=>\(x=\dfrac{11}{15}:\dfrac{2}{5}=\dfrac{11}{15}\cdot\dfrac{5}{2}=\dfrac{11}{3\cdot2}=\dfrac{11}{6}\)
\(-\frac{28}{35}\) < 0
\(\frac{16}{20}\) > 0
vậy - \(\frac{28}{35}\) < \(\frac{16}{20}\) nên \(-\frac{28}{35}\) = \(\frac{16}{20}\) là sai.
P= 1-1/2+1/3-1/4+1/5-...-1/2024
P= (1+1/2+1/3+1/4+...+1/2024) - 2(1/2+1/4+1/6+...+1/2024)
P= (1+1/2+1/3+1/4+...+1/2024) - (1+1/2+1/3+...+1/1012)
P= 1/1013+1/1014+...+1/2024
Vậy P=Q
Chúc bạn học tốt nhé!
P= 1-1/2+1/3-1/4+1/5-...-1/2024 P= (1+1/2+1/3+1/4+...+1/2024) - 2(1/2+1/4+1/6+...+1/2024) P= (1+1/2+1/3+1/4+...+1/2024) - (1+1/2+1/3+...+1/1012) P= 1/1013+1/1014+...+1/2024 Vậy P=Q Chúc bạn học tốt nhé!
A = \(\frac{2024}{2025}\) + \(\frac{2025}{2026}\)
B = \(\frac{2024+2025}{2025+2026}=\) \(\frac{2024}{2025+2026}+\frac{2025}{2025+2026}\)
\(\frac{2024}{2025+2026}<\frac{2024}{2025}\)
\(\frac{2025}{2025+2026}<\frac{2025}{2025+2026}\)
B = \(\frac{2024}{2025+2026}+\frac{2025}{2025+2026}\) < \(\frac{2024}{2025}+\frac{2025}{2026}\) = A
Vậy B < A