5/2+ 5/4 + 5/8 + 5/16 + 5 /32 + 5/64
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\(\frac{2}{3}+\frac{2}{5}\div\frac{5}{4}\)
\(=\frac{2}{3}+\frac{2}{5}\times\frac{4}{5}\)
\(=\frac{2}{3}+\frac{8}{25}\)
\(=\frac{74}{75}\)
~ Chúc bạn học tốt ~
\(\dfrac{4}{5}\) : (\(\dfrac{4}{5}\) .- \(\dfrac{5}{4}\)) : (\(\dfrac{16}{25}\) - \(\dfrac{1}{5}\))
= \(\dfrac{4}{5}\) : (-1) : (\(\dfrac{16}{25}\) - \(\dfrac{5}{25}\))
= -\(\dfrac{4}{5}\) : \(\dfrac{11}{25}\)
= - \(\dfrac{4}{5}\) x \(\dfrac{25}{11}\)
= - \(\dfrac{20}{11}\)
\(\dfrac{4}{5}\): (\(\dfrac{4}{5}\).-\(\dfrac{5}{4}\)) : (\(\dfrac{16}{25}\) - \(\dfrac{1}{5}\))
=\(\dfrac{4}{5}\) x - 1: (\(\dfrac{16}{25}\) - \(\dfrac{5}{25}\))
= - \(\dfrac{4}{5}\) : \(\dfrac{11}{25}\)
= - \(\dfrac{4}{5}\) x \(\dfrac{25}{11}\)
= - \(\dfrac{20}{11}\)
\(\dfrac{11}{12}\): (\(\dfrac{7}{9}\) + - \(\dfrac{1}{3}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{5}{15}\))
= \(\dfrac{11}{12}\) : (\(\dfrac{7}{9}\) - \(\dfrac{3}{9}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{1}{3}\))
= \(\dfrac{11}{12}\) : \(\dfrac{4}{9}\) - \(\dfrac{1}{3}\)
= \(\dfrac{11}{12}\) x \(\dfrac{9}{4}\) - \(\dfrac{1}{3}\)
= \(\dfrac{99}{48}\) - \(\dfrac{16}{48}\)
= \(\dfrac{83}{48}\)
\(5^{333}=\left(5^3\right)^{111}=125^{111}\)
\(3^{555}=\left(3^5\right)^{111}=243^{111}\)
Vì 125 < 243 => 125111 < 243111
Vậy \(5^{333}<3^{555}\).
\(5^{333}=5^{3\cdot111}=\left(5^3\right)^{111}=125^{111}\)
\(3^{555}=3^{5\cdot111}=\left(3^5\right)^{111}=243^{111}\)
Vì \(125^{111}<243^{111}\)
Nên \(5^{333}<3^{555}\)
b: A=1/3+1/9+...+1/3^10
=>3A=1+1/3+...+1/3^9
=>A*2=1-1/3^10=(3^10-1)/3^10
=>A=(3^10-1)/(2*3^10)
c: C=3/2+3/8+3/32+3/128+3/512
=>4C=6+3/2+...+3/128
=>3C=6-3/512
=>C=1023/512
d: A=1/2+...+1/256
=>2A=1+1/2+...+1/128
=>A=1-1/256=255/256
5/2 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64
= 5(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64)
Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
=> 2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32
=> 2A - A = 1 - 1/64
=> A = 1 - 1/64
Do đó : 5(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64) = 5(1 - 1/64) = 5 . 63/64 = 315/64
nhanh len gium minh duoc ko