C = 1 - 2 + 22 - 23 + 24 - ... + 22022
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Những câu hỏi liên quan
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
1 tháng 9 2023
Bài 1
a, cm : A = 165 + 215 ⋮ 3
A = 165 + 215
A = (24)5 + 215
A = 220 + 215
A = 215.(25 + 1)
A = 215. 33 ⋮ 3 (đpcm)
b,cm : B = 88 + 220 ⋮ 17
B = (23)8 + 220
B = 216 + 220
B = 216.(1 + 24)
B = 216. 17 ⋮ 17 (đpcm)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
1 tháng 9 2023
c, cm: C = 1 - 2 + 22 - 23 + 24 - 25 + 26 -...-22021 + 22022 : 6 dư 1
C=1+(-2+22-23+24- 25+26)+...+(-22017+22018-22019+22020-22021+22022)
C = 1 + 42 +...+ 22016.(-2 + 22 - 23 + 24 - 25 + 26)
C = 1 + 42+...+ 22016.42
C = 1 + 42.(20+...+22016)
42 ⋮ 6 ⇒ C = 1 + 42.(20+...+22016) : 6 dư 1 đpcm
NH
1
NV
Nguyễn Việt Lâm
Giáo viên
28 tháng 12 2021
\(A=1+2+2^2+...+2^{2022}\)
\(\Rightarrow2A=2+2^2+...+2^{2023}\)
\(\Rightarrow2A-A=2^{2023}-1\)
\(\Rightarrow A=2^{2023}-1\)
\(\Rightarrow A< 2^{2023}=2^2.2^{2021}=4.2^{2021}< 5^{2021}\)
\(\Rightarrow A< B\)
NC
2
ND
Nguyễn Đức Trí
VIP
29 tháng 7 2023
a) \(S=1+2+2^2+2^3+...+2^{2022}=\dfrac{2^{2022+1}-1}{2-1}=2^{2023}-1\)
b) \(S=1+4+4^2+4^3+...+4^{2022}=\dfrac{4^{2022+1}-1}{4-1}=\dfrac{4^{2023}-1}{3}\)
29 tháng 7 2023
\(S=1+2+2^2+2^3+...+2^{2022}\\ 2S=2+2^2+2^3+2^4+...+2^{2023}\\ 2S-S=2+2^2+2^3+2^4+...+2^{2023}-1-2-2^2-2^3-...-2^{2022}\\ S=2^{2023}-1\\ S=4+4^2+4^3+...+4^{2022}\\ 4S=4^2+4^3+4^4+...+4^{2023}\\ 4S-S=4^2+4^3+4^4+...+4^{2023}-4-4^2-4^3-...-4^{2023}\\ 3S=4^{2023}-4\\ S=\dfrac{4^{2023}-4}{3}\)
HT
1
30 tháng 10 2023
\(A=2+2^2+2^3+...+2^{2021}\)
=>\(2A=2^2+2^3+2^4+...+2^{2022}\)
=>\(2A-A=2^2+2^3+...+2^{2021}+2^{2022}-2-2^2-2^3-...-2^{2021}\)
=>\(A=2^{2022}-2\)
=>A<B
AH
Akai Haruma
Giáo viên
31 tháng 12 2023
Câu 1:
$A=(2+2^2)+(2^3+2^4)+(2^5+2^6)+....+(2^{2019}+2^{2020})$
$=2(1+2)+2^3(1+2)+2^5(1+2)+....+2^{2019}(1+2)$
$=(1+2)(2+2^3+2^5+...+2^{2019})=3(2+2^3+2^5+...+2^{2019})\vdots 3$
-----------------
$A=2+(2^2+2^3+2^4)+(2^5+2^6+2^7)+....+(2^{2018}+2^{2019}+2^{2020})$
$=2+2^2(1+2+2^2)+2^5(1+2+2^2)+....+2^{2018}(1+2+2^2)$
$=2+(1+2+2^2)(2^2+2^5+....+2^{2018})$
$=2+7(2^2+2^5+...+2^{2018})$
$\Rightarrow A$ chia $7$ dư $2$.
AH
Akai Haruma
Giáo viên
31 tháng 12 2023
Câu 2:
$B=(3+3^2)+(3^3+3^4)+....+(3^{2021}+3^{2022})$
$=3(1+3)+3^3(1+3)+...+3^{2021}(1+3)$
$=(1+3)(3+3^3+...+3^{2021})=4(3+3^3+....+3^{2021})\vdots 4$
-------------------
$B=(3+3^2+3^3)+(3^4+3^5+3^6)+...+(3^{2020}+3^{2021}+3^{2022})$
$=3(1+3+3^2)+3^4(1+3+3^2)+....+3^{2020}(1+3+3^2)$
$=(1+3+3^2)(3+3^4+...+3^{2020})=13(3+3^4+...+3^{2020})\vdots 13$ (đpcm)
VV
3
T
19 tháng 10 2023
\(A=2+2^2+2^3+...+2^{2020}+2^{2021}+2^{2022}\\=(2+2^2)+(2^3+2^4)+(2^5+2^6)+...+(2^{2021}+2^{2022})\\=2\cdot(1+2)+2^3\cdot(1+2)+2^5\cdot(1+2)+...+2^{2021}\cdot(1+2)\\=2\cdot3+2^3\cdot3+2^5\cdot3+...+2^{2021}\cdot3\\=3\cdot(2+2^3+2^5+..+2^{2021})\)
Vì \(3\cdot\left(2+2^3+2^5+...+2^{2021}\right)⋮3\)
nên \(A⋮3\).
\(Toru\)
TN
19 tháng 10 2023
A=(2+22)+22(2+22)+...+22020(2+22)
A= 6.1+22.6+...+22020.6
A=6(1+22+...+22020) chia hết cho 3
vậy A chia hết cho 3
LT
Lương Thị Vân Anh
CTVHS
25 tháng 7 2023
Ta có \(A=\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+...+\dfrac{2022}{2^{2022}}+\dfrac{2023}{2^{2023}}\)
\(2A=1+\dfrac{2}{2}+\dfrac{3}{2^2}+...+\dfrac{2022}{2^{2021}}+\dfrac{2023}{2^{2022}}\)
\(2A-A=\left(1+\dfrac{2}{2}+\dfrac{3}{2^2}+...+\dfrac{2022}{2^{2021}}+\dfrac{2023}{2^{2022}}\right)-\left(\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+...+\dfrac{2022}{2^{2022}}+\dfrac{2023}{2^{2023}}\right)\)\(A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2021}}+\dfrac{1}{2^{2022}}\) - \(\dfrac{2023}{2^{2023}}\)
Đặt B = \(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2021}}+\dfrac{1}{2^{2022}}\)
2B = \(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^{2020}}+\dfrac{1}{2^{2021}}\)
2B - B = \(\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^{2020}}+\dfrac{1}{2^{2021}}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2021}}+\dfrac{1}{2^{2022}}\right)\)B = 2 - \(\dfrac{1}{2^{2022}}\)
Suy ra A = 2 - \(\dfrac{1}{2^{2022}}\) - \(\dfrac{2023}{2^{2023}}\) < 2
Vậy A < 2
25 tháng 7 2023
\(A=\dfrac{1}{2}+\dfrac{2}{2^{2}}+\dfrac{3}{2^{3}}+...+\dfrac{2022}{2^{2022}}+\dfrac{2023}{2^{2023}}\)
\(2A=1+\dfrac22+\dfrac3{2^2}\ +\,.\!.\!.+\ \dfrac{2022}{2^{2021}}+\dfrac{2023}{2^{2022}}\\2A-A=\left(1+\dfrac22+\dfrac3{2^2}\ +\,.\!.\!.+\ \dfrac{2022}{2^{2021}}+\dfrac{2023}{2^{2022}}\right)-\left(\dfrac12+\dfrac2{2^2}+\dfrac3{2^3}\ +\,.\!.\!.+\ \dfrac{2022}{2^{2022}}+\dfrac{2023}{2^{2023}}\right)\\A=1+\dfrac12+\dfrac1{2^3}\ +\,.\!.\!.+\ \dfrac1{2^{2021}}+\dfrac1{2^{2022}}-\dfrac{2023}{2^{2023}}\\2\left(A+\dfrac{2023}{2^{2023}}\right)=2+1+\dfrac12+\dfrac1{2^2}\ +\,.\!.\!.+\ \dfrac1{2^{2020}}+\dfrac1{2^{2021}}\\A+\dfrac{2023}{2^{2023}}=2-\dfrac1{2^{2022}}\\A=2-\dfrac1{2^{2022}}+\dfrac{2023}{2^{2023}}<2\)
Lời giải:
$C=1-2+2^2-2^3+2^4-....+2^{2022}$
$2C=2-2^2+2^3-2^4+2^5-...+2^{2023}$
$\Rightarrow C+2C=(1-2+2^2-2^3+2^4-....+2^{2022})+(2-2^2+2^3-2^4+2^5-...+2^{2023})$
$\Rightarrow 3C=2^{2023}-1$
$\Rightarrow C=\frac{2^{2023}-1}{3}$