chứng tỏ A=1/1 ✖ 2+1/2 ✖ 3+...+1/99 ✖ 100<1
( 1 - \(\dfrac{1}{2}\) ) ✖ ( 1 - \(\dfrac{1}{3}\) ) ✖ ( 1 - \(\dfrac{1}{4}\) ) ✖ ( 1 - \(\dfrac{1}{5}\) ) ✖ ( 1 - \(\dfrac{1}{6}\) ) ✖ ( 1 - \(\dfrac{1}{7}\) ) ✖ (1 - \(\dfrac{1}{8}\))
\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{7}{8}=\dfrac{1}{8}\)
`= 1/2 xx 2/3 xx...xx 7/8`
`= 1/8`
\(=\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times...\times\dfrac{6}{7}\times\dfrac{7}{8}\\ =\dfrac{1}{8}\)
B=(1-\(\dfrac{1}{3}\)) ✖(1-\(\dfrac{1}{6}\))✖(1-\(\dfrac{1}{10}\))✖(1-\(\dfrac{1}{15}\))✖....✖(1-\(\dfrac{1}{780}\))
\(B=\left(1-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{6}\right)\cdot\left(1-\dfrac{1}{10}\right)\cdot\left(1-\dfrac{1}{15}\right)\cdot...\cdot\left(1-\dfrac{1}{780}\right)\)
\(B=\left(1-\dfrac{1}{3+6+10+15+...+780}\right)\)
\(B=\left(1-\dfrac{1}{\left(780-3\right)\div3+1}\right)\)
\(B=\left(1-\dfrac{1}{260}\right)\)
\(B=\dfrac{259}{260}\)
\(\dfrac{-5}{13}\)✖\(\dfrac{3}{7}\)-\(\dfrac{2}{17}\)✖\(\dfrac{8}{13}\)+\(\dfrac{5}{13}\)✖\(\dfrac{1}{7}\)
Giải hộ mình nhé có cả lời giải đấy
ok.mình cho 1 tim
Ta có: \(\dfrac{-5}{13}\cdot\dfrac{3}{7}-\dfrac{2}{17}\cdot\dfrac{8}{13}+\dfrac{5}{13}\cdot\dfrac{1}{7}\)
\(=\dfrac{5}{13}\left(-\dfrac{3}{7}+\dfrac{1}{7}\right)-\dfrac{2}{17}\cdot\dfrac{8}{13}\)
\(=\dfrac{5}{13}\cdot\dfrac{-2}{7}-\dfrac{2}{17}\cdot\dfrac{8}{13}\)
\(=\dfrac{-10}{91}-\dfrac{16}{221}\)
\(=\dfrac{-282}{1547}\)
\(\dfrac{-5}{13}.\dfrac{3}{7}-\dfrac{2}{17}.\dfrac{8}{13}+\dfrac{5}{13}.\dfrac{1}{7}\)
\(=\dfrac{5}{13}.\dfrac{-3}{7}-\dfrac{2}{17}.\dfrac{8}{13}+\dfrac{5}{13}.\dfrac{1}{7}\)
\(=\dfrac{5}{13}.\left(\dfrac{-3}{7}+\dfrac{1}{7}\right)+\dfrac{-2}{17}.\dfrac{8}{13}\)
\(=\dfrac{5}{13}.\dfrac{-2}{7}+\dfrac{-2}{13}.\dfrac{8}{17}\)
\(=\dfrac{-2}{13}.\dfrac{5}{7}+\dfrac{-2}{13}.\dfrac{8}{17}\)
\(=\dfrac{-2}{13}.\left(\dfrac{5}{7}+\dfrac{8}{17}\right)\)
\(=\dfrac{-2}{13}.\dfrac{141}{119}\)
\(=\dfrac{-282}{1547}\)
Tìm x
x ✖ 3 ✖ \(\dfrac{1}{3}\)= \(2\dfrac{2}{3}\) giúp với mik cần gấp
⇔\(x\) x 1=\(\dfrac{8}{3}\)
⇔\(x\) =\(\dfrac{8}{3}\)
Vậy \(x\)=\(\dfrac{8}{3}\)
\(x\times3\times\dfrac{1}{3}=2\dfrac{2}{3}\\x\times3\times\dfrac{1}{3}=\dfrac{8}{3}\\ x\times3=\dfrac{8}{3}:\dfrac{1}{3}\\ x\times3=8\\ x=8:3\\ x=\dfrac{8}{3}\)
\(\Rightarrow x=\dfrac{8}{3}\)
Tìm y
y ✖ 2 + y ✖ \(\dfrac{1}{5}\) = \(1\dfrac{3}{5}\) giúp mik với mik cần rất chi là gấp
\(\Rightarrow y\times\left(2+\dfrac{1}{5}\right)=\dfrac{8}{5}\\ \Rightarrow y\times\dfrac{11}{5}=\dfrac{8}{5}\\ \Rightarrow y=\dfrac{8}{5}:\dfrac{11}{5}=\dfrac{8}{5}\times\dfrac{5}{11}=\dfrac{8}{11}\)
tính
\(\sqrt{2}\) ✖ (\(\sqrt{21}+3\)) ✖ \(\sqrt{5-\sqrt{21}}\)
\(\sqrt{2}\times\left(\sqrt{5}-1\right)\times\sqrt{3+\sqrt{5}}\)
Tính giá trị biểu thức bằng 2 cách
(2,45+7,55)✖ 2,75
(25,5-17,15)✖ 100
5 ✖ 67,35 ✖ 20
Giúp mình nha vội lắm ai nhanh nhất mình tích cho
C1 : ( 2,45 + 7,55 ) x 2,75
= 10 x 2,75
= 27,5
C2 : ( 2,45 + 7,55 ) x 2,75
= 2,45 x 2,75 + 7,55 x 2,75
= 6,7375 + 20,7625
= 27,5
C1 : ( 25,5 - 17,15 ) x 100
= 8,35 x 100
= 835
C2 : ( 25,5 - 17,15 ) x 100
= 25,5 x 100 - 17,15 x 100
= 2550 - 1715
= 835
C1 : 5 x 67,35 x 20
= 336,75 x 20
= 6735
C2 : 5 x 67,35 x 20
= 5 x 20 x 67,35
= 100 x 67,35
= 6735
5/6 ✖ x - 2/3 = 1/4 ✖ x + 2/3
giúp mình với mình đang cần
cảm ơn nhiều nha
Nhân cả hai vế với 12 (đỡ mất công quy đồng kiểu kia), ta tìm x sao cho:
\(10x-8=3x+8\Leftrightarrow7x=16\Leftrightarrow x=\frac{16}{7}\)
Vậy...