\(\dfrac{2}{2^{100}}\) = \(\dfrac{1}{2^{99}}\) Đúng hay sai
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5 tháng 7 2023
Đặt \(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{99^2}+\dfrac{1}{100^2}\)
\(< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{98.99}+\dfrac{1}{99.100}\)
\(B=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{98.99}+\dfrac{1}{99.100}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{98}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1-\dfrac{1}{100}=\dfrac{99}{100}\) \(\Rightarrow A< \dfrac{99}{100}\)
\(1-\dfrac{1}{2^2}-\dfrac{1}{3^2}-...-\dfrac{1}{100^2}=1-\left(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{100^2}\right)=1-A>\dfrac{1}{100}\)
3 tháng 8 2021
bài này bn trục căn thức mẫu nhé
\(P=\dfrac{1-\sqrt{2}}{1-2}+\dfrac{\sqrt{2}-\sqrt{3}}{2-3}+...+\dfrac{\sqrt{99}-\sqrt{100}}{99-100}\)
\(P=\dfrac{1-\sqrt{2}+\sqrt{2}-\sqrt{3}+....+\sqrt{99}-\sqrt{100}}{-1}=\dfrac{1-\sqrt{100}}{-1}=\sqrt{100}-1\)
\(=10-1=9\)
TA
3 tháng 8 2021
`=(\sqrt1-\sqrt2)/(1-2)+(\sqrt2-\sqrt3)/(2-3)+.....+(\sqrt99-\sqrt100)/(99-100)`
`=\sqrt2-\sqrt1+\sqrt3-\sqrt2+.....+\sqrt100-\sqrt99`
`=-\sqrt1+\sqrt100=-1+10=9`
LT
2 tháng 5 2017
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10 tháng 5 2017
cho đường cao của ba tam giác lần lượt là 4, 12 và x . tìm x biết x là một số tự nhiên
18 tháng 9 2021
\(\dfrac{1}{2^2}< \dfrac{1}{1\cdot2};\dfrac{1}{3^2}< \dfrac{1}{2\cdot3};...;\dfrac{1}{100^2}< \dfrac{1}{99\cdot100}\\ \Rightarrow\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< \dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{99\cdot100}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}=1-\dfrac{1}{100}=\dfrac{99}{100}< 1\\ \RightarrowĐpcm\)
1 tháng 11 2017
\(A=\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+...+\dfrac{99}{2^{99}}+\dfrac{100}{2^{100}}\)
\(2A=1+1+\dfrac{3}{2^2}+...+\dfrac{99}{2^{98}}+\dfrac{100}{2^{99}}\)
\(2A-A=\left(1+1+\dfrac{3}{2^2}+...+\dfrac{99}{2^{98}}+\dfrac{100}{2^{99}}\right)-\left(\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+...+\dfrac{99}{2^{99}}+\dfrac{100}{2^{100}}\right)\)
\(A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{98}}+\dfrac{1}{2^{99}}-\dfrac{100}{2^{100}}\)
Đặt:
\(B=1+\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{98}}+\dfrac{1}{2^{99}}\)
\(2B=2+1+\dfrac{1}{2^2}+....+\dfrac{1}{2^{97}}+\dfrac{1}{2^{98}}\)
\(2B-B=\left(2+1+\dfrac{1}{2^2}+....+\dfrac{1}{2^{97}}+\dfrac{1}{2^{98}}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{98}}+\dfrac{1}{2^{99}}\right)\)
\(B=2-\dfrac{1}{2^{99}}\)
Vậy \(A=2-\dfrac{1}{2^{99}}-\dfrac{100}{2^{100}}< 2\)
1 tháng 11 2017
Bây giờ mình đang bận học bài 1 chút.Xíu nữa mình làm cho nhé
14 tháng 7 2023
Ta đặt
\(A=\dfrac{7}{1\times2}+\dfrac{7}{2\times3}+...+\dfrac{7}{99\times100}\)
\(\dfrac{1}{7}\times A=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+....+\dfrac{1}{99\times100}\)
\(\dfrac{1}{7}\times A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{99}-\dfrac{1}{100}\)
\(\dfrac{1}{7}\times A=1-\dfrac{1}{100}\)
\(\dfrac{1}{7}\times A=\dfrac{99}{100}\)
\(A=\dfrac{99}{100}\div\dfrac{1}{7}\)
\(A=\dfrac{693}{100}\)
KV
14 tháng 7 2023
= 7.(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100)
= 7.(1 - 1/100)
= 7 . 99/100
= 693/100
16 tháng 3 2023
\(u_1=\dfrac{1}{\sqrt{2}};q=\dfrac{1}{\sqrt{2}}\)
\(S_{99}=\dfrac{\dfrac{1}{\sqrt{2}}\cdot\left(\dfrac{1}{\sqrt{2}}^{99}-1\right)}{\dfrac{1}{\sqrt{2}}-1}=\dfrac{1}{\sqrt{2}}\cdot\left(\dfrac{1-2^{49}\cdot\sqrt{2}}{2^{49}\cdot\sqrt{2}}\right):\dfrac{1-\sqrt{2}}{\sqrt{2}}\)
\(=\dfrac{1}{1-\sqrt{2}}\cdot\dfrac{1-2^{49}\cdot\sqrt{2}}{2^{49}\cdot\sqrt{2}}\)
đúng
Đúng. Vì khi ta quy đồng lên ta có
1/299=1.2/299.2=2/2100
Vậy 2/2100=1/299
Chúc bạn học tốt!