Cho B= 24.(52 + 1) (54 + 1)......(532 + 1) - 564
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31 tháng 8 2021
\(C=48\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)=2\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)=2\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\left(5^{128}-1\right)=2.5^{128}-2\)
31 tháng 8 2021
c: Ta có: \(C=48\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\cdot\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^2-1\right)\left(5^2+1\right)\cdot\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{16}-1\right)\cdot\left(5^{16}+1\right)\cdot\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{32}-1\right)\left(5^{32}+1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{64}-1\right)\left(5^{64}+1\right)\)
\(=2\cdot\left(5^{128}-1\right)\)
\(=2\cdot5^{128}-2\)
HL
2
6 tháng 10 2023
`#3107.101107`
Gọi biểu thức trên là A
Ta có:
\(A=1+5^2+5^4+...+5^{40}\\ =1\cdot\left(1+5^2\right)+5^4\cdot\left(1+5^2\right)+...+5^{38}\cdot\left(1+5^2\right)\\ =\left(1+5^2\right)\cdot\left(1+5^4+...+5^{38}\right)\\ =26\cdot\left(1+5^4+...+5^{38}\right)\)
Vì \(26\cdot\left(1+5^4+...+5^{38}\right)\text{ }⋮\text{ }26\)
\(\Rightarrow A\text{ }⋮\text{ }26\)
_______
Gọi biểu thức trên là B
Ta có:
\(B=1+2^2+2^4+...+2^{100}\\ =1\cdot\left(1+2^2+2^4\right)+2^6\cdot\left(1+2^2+2^4\right)+...+2^{96}\cdot\left(1+2^2+2^4\right)\\ =\left(1+2^2+2^4\right)\cdot\left(1+2^6+...+2^{96}\right)\\ =21\cdot\left(1+2^6+...+2^{96}\right)\)
Vì \(21\cdot\left(1+2^6+...+2^{96}\right)\text{ }⋮\text{ }21\)
\(\Rightarrow B\text{ }⋮\text{ }21\)
_______
Gọi biểu thức trên là C
Ta có:
\(C=1+3^2+3^4+...+3^{100}\\ =1\cdot\left(1+3^2+3^4+3^6\right)+3^6\cdot\left(1+3^2+3^4+3^6\right)+...+3^{94}\cdot\left(1+3^2+3^4+3^6\right)\\ =\left(1+3^2+3^4+3^6\right)\cdot\left(1+3^6+...+3^{94}\right)\\ =820\cdot\left(1+3^6+...+3^{94}\right)\)
Vì \(820\cdot\left(1+3^6+...+3^{94}\right)\text{ }⋮\text{ }82\)
\(\Rightarrow C\text{ }⋮\text{ }82.\)
6 tháng 10 2023
a) \(A=1+5^2+5^4+5^6...+5^{40}\)
\(\Rightarrow A=\left(1+5^2\right)+5^4\left(1+5^2\right)+...+5^{38}\left(1+5^2\right)\)
\(\Rightarrow A=26+5^4.26+...+5^{38}.26\)
\(\Rightarrow A=26\left(1+5^4+...+5^{38}\right)⋮26\)
\(\Rightarrow1+5^2+5^4+5^6...+5^{40}⋮6\left(dpcm\right)\)
b) \(B=1+2^2+2^4+2^6+...+2^{100}\)
\(\Rightarrow B=\left(1+2^2+2^4\right)+2^6\left(1+2^2+2^4\right)+...+2^{96}\left(1+2^2+2^4\right)\)
\(\Rightarrow B=21+2^6.21+...+2^{96}.21\)
\(\Rightarrow B=21\left(1+2^6+...+2^{96}\right)⋮21\)
\(\Rightarrow1+2^2+2^4+2^6+...+2^{100}⋮21\left(dpcm\right)\)
Bài C tương tự bạn tự làm nhé!
H9
HT.Phong (9A5)
CTVHS
17 tháng 10 2023
\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)
Đặt \(\left(1\right)=A\)
\(\Rightarrow A=1+5^2+...+5^{2x}\)
\(\Rightarrow5^2A=5^2+5^4+...+5^{2x+2}\)
\(\Rightarrow25A=5^2+5^4+...+5^{2x+2}\)
\(\Rightarrow25A-A=5^2+5^4+...+5^{2x+2}-1-5^2-...-5^{2x}\)
\(\Rightarrow24A=5^{2x+2}-1\)
\(\Rightarrow A=\dfrac{5^{2x+2}-1}{24}\)
Mà: \(A=\dfrac{25^6-1}{24}\)
\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)
\(\Rightarrow5^{2x+2}-1=5^{12}-1\)
\(\Rightarrow5^{2x+2}=5^{12}\)
\(\Rightarrow2x+2=12\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=\dfrac{10}{2}\)
\(\Rightarrow x=5\)
25 tháng 8 2021
\(a,2^2=4,2^3=8,2^4=16,2^5=32,2^6=64,2^7=128,2^8=256,2^9=512,2^{10}=1024\)
\(b,3^2=9,3^3=27,3^4=81,3^5=243\)
\(c,4^2=16,4^3=64,4^4=256\)
\(d,5^2=25,5^3=125,5^4=625\)
12 tháng 12 2021
Bài 1:
\(a,A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{2009}+2^{2010}\right)\\ A=\left(1+2\right)\left(2+2^3+...+2^{2009}\right)=3\left(2+...+2^{2009}\right)⋮3\\ A=\left(2+2^2+2^3\right)+...+\left(2^{2008}+2^{2009}+2^{2010}\right)\\ A=\left(1+2+2^2\right)\left(2+...+2^{2008}\right)=7\left(2+...+2^{2008}\right)⋮7\)
\(b,\left(\text{sửa lại đề}\right)B=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{2009}+3^{2010}\right)\\ B=\left(1+3\right)\left(3+3^3+...+3^{2009}\right)=4\left(3+3^3+...+3^{2009}\right)⋮4\\ B=\left(3+3^2+3^3\right)+...+\left(3^{2008}+3^{2009}+3^{2010}\right)\\ B=\left(1+3+3^2\right)\left(3+...+3^{2008}\right)=13\left(3+...+3^{2008}\right)⋮13\)
12 tháng 12 2021
Bài 2:
\(a,\Rightarrow2A=2+2^2+...+2^{2012}\\ \Rightarrow2A-A=2+2^2+...+2^{2012}-1-2-2^2-...-2^{2011}\\ \Rightarrow A=2^{2012}-1>2^{2011}-1=B\\ b,A=\left(2020-1\right)\left(2020+1\right)=2020^2-2020+2020-1=2020^2-1< B\)
AH
Akai Haruma
Giáo viên
16 tháng 12 2023
Bài 1:
$B=1+3+3^2+3^3+...+3^{100}$
$=1+(3+3^2)+(3^3+3^4)+...+(3^{99}+3^{100})$
$=1+3(1+3)+3^3(1+3)+...+3^{99}(1+3)$
$=1+(1+3)(3+3^3+...+3^{99})=1+4(3+3^3+....+3^{99})$
$\Rightarrow B$ chia 4 dư 1.
AH
Akai Haruma
Giáo viên
16 tháng 12 2023
Bài 2:
$C=5-5^2+5^3-5^4+...+5^{2023}-5^{2024}$
$5C=5^2-5^3+5^4-5^5+...+5^{2024}-5^{2025}$
$\Rightarrow C+5C=5-5^{2025}$
$6C=5-5^{2025}$
$C=\frac{5-5^{2025}}{6}$
24 tháng 12 2015
a, 54 x 113 + 54 x 113 + 113
= 113 x ( 54 + 54 + 1 )
= 113 x 109
= 12 317
b, ( 532 x 7 - 266 x 14 ) x ( 532 x 7 + 266 )
= ( 266 x 2 x 7 - 266 x 14 ) - ( 532 x 7 + 266 )
= 266 x ( 2 x 7 - 14 )
= 266 x ( 14 - 14 )
= 266 x 0
= 0
c, 117 x ( 36 + 62 ) - 17 x ( 62 + 36 )
= 117 x 98 - 17 x 98
= 98 x ( 117 - 17 )
= 98 x 100
= 9800
d, ( 145 x 99 + 145 ) - ( 143 x 101 - 143 )
= 145 x ( 99 + 1 ) - 143 x ( 101 - 1 )
= 145 x 100 - 143 x 100
= 14500 - 14300
= 200
e, 45 x 16 - 17
______________
45 x 15 + 28
Ta có : 45 x 16 - 17
= 720 - 17
= 703
Ta có : 45 x 15 + 28
= 675 + 28
= 703
Vậy 45 x 16 - 17 703
______________ = _____________ = 1
45 x 15 + 28 703
( * giải thích thêm : __________ chính là dấu chia đó )
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
7 tháng 11 2023
Đề bài thiếu yêu cầu cụ thể em nhé. em cập nhật lại câu hỏi để được sự hỗ trợ tốt nhất cho tài khoản olm vip
CM
5 tháng 11 2019
Lời giải chi tiết:
| 45 + 3 < 50 | 54 – 2 < 54 + 2 |
| 45 + 30 = 35 + 40 | 54 – 20 > 52 – 40 |
| 45 + 34 = 34 + 45 | 54 – 24 > 45 – 24 |
CG
10 tháng 10 2021
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\(B=24.\left(5^2+1\right)\left(5^4+1\right)......\left(5^{32}+1\right)-5^{64}\)
\(B=\left(5^2-1\right)\left(5^2+1\right)....\left(5^{32}+1\right)-5^{64}\)
\(B=\left(5^4-1\right).....\left(5^{32}+1\right)-5^{64}\)
\(B=\left(5^{32}-1\right)\left(5^{32}+1\right)-5^{64}\)
\(B=5^{64}-1-5^{64}\)
\(B=-1\)