12345 +12344 = ?
CM: 12345678-12345677 chia hết cho 12344
12345^678 - 12345^677 = 12345^677( 12345 - 1) = 12345^677. 12344 chia hết cho 12344 => 12345^678 - 12345^677 chia hết cho 12344
Chứng minh rằng 12345678 - 12345677 chia hết cho 12344
1-2+3-4+5-6+7-8+....+12343-12344+12345
1-2+3-4+5-6+7-8+....+12343-12344+12345
=(1-2)+(3-4)+(5-6)+(7-8)+....+(12343-12344)+12345
=(-1)+(-1)+(-1)+(-1)+....+(-1)+12345
=(-1)*6172+12345
=-6172+12345
=6173 nha bạn !!!!!!!!!!!!!!!!!!!!!!!!!
\(\left(1-2\right)+\left(3-4\right)+...+\left(12343-12344\right)+12345\)
\(\left(-1\right)-1-1-...-1+12345\) có 6172 số -1
-6172+12345=6173
chứng minh rằng
a, 2008 ^100 +2008^99 chia hết cho 2009
b, 12345^678 -12345^677 chia hết cho 12344
a) Ta có:
\(2008^{100}+2008^{99}\)
\(=2008^{99}.\left(2008+1\right)\)
\(=2008^{99}.2009\)
Vì \(2009⋮2009\) nên \(2008^{99}.2009⋮2009.\)
\(\Rightarrow2008^{100}+2008^{99}⋮2009.\)
b) Ta có:
\(12345^{678}-12345^{677}\)
\(=12345^{677}.\left(12345-1\right)\)
\(=12345^{677}.12344\)
Vì \(12344⋮12344\) nên \(12345^{677}.12344⋮12344.\)
\(\Rightarrow12345^{678}-12345^{677}⋮12344.\)
Chúc bạn học tốt!
chứng minh
a/\(^{2008^{100}+2008^{99}⋮2009}\)
b/\(12345^{678}-12345^{677}⋮12344\)
a, 2008\(-⋮\)-1(mod 2009)
\(2008^{100}-⋮1\left(mod2009\right)\)
\(2008^{99}-⋮-1\left(mod2009\right)\)
=>\(2008^{100}+2008^{99}⋮2009\)
b,\(12345-⋮1\left(mod12344\right)\)
\(12345^{678}-⋮1\left(mod12344\right)\)
\(12345^{677}-⋮1\left(mod12344\right)\)
\(12345^{678}+12345^{677}không⋮12344\)(đề sai)
\(-⋮\)là đồng dư nha
12345 . 98765 - 86420 / 12345 + 12344 . 98765
ai đó giúp mình với viết cả cách lam luôn nha !!!
1 c/m \(2008^{100}+2008^{99}\)chia hết cho 2009
\(12345^{678}-12345^{677}\)chia hết cho 12344
ta có: 2008100 + 200899 = 200899.(2008+1) = 200899.2009 chia hết cho 2009
=> 2008100 + 200899 chia hết cho 2009 ( đ p c m)
ta có: 12345678 -12345677 = 12345677.(12345-1) = 12345677.12344 chia hết cho 12344
=> đ p c m
\(2008^{100}+2008^{99}=2008^{99}.\left(2008+1\right)=2008^{99}.2009\)
Mà \(2009⋮2009\Rightarrow2008^{99}.2009⋮2009\)
Vậy \(2008^{100}+2008^{99}\)chia hết cho 2009 ( đpcm )
\(12345^{678}-12345^{677}=12345^{677}.\left(12345-1\right)=12345^{677}.12344\)
Mà \(12344⋮12344\Rightarrow12345^{677}.12344⋮12344\)
Vậy \(12345^{678}-12345^{677}\)chia hết cho 12344 ( đpcm )
So sánh:A=\(\frac{10^{12345}+1}{10^{12346}+1}\)
B=\(\frac{10^{12344}+1}{10^{12345}+1}\)
Ta có công thức :
\(\frac{a}{b}< \frac{a+c}{b+c}\)\(\left(\frac{a}{b}< 1;a,b,c\inℕ^∗\right)\)
Áp dụng vào ta có :
\(A=\frac{10^{12345}+1}{10^{12346}+1}< \frac{10^{12345}+1+9}{10^{12346}+1+9}=\frac{10^{12345}+10}{10^{12346}+10}=\frac{10\left(10^{12344}+1\right)}{10\left(10^{12345}+1\right)}=\frac{10^{12344}+1}{10^{12345}+1}=B\)
\(\Rightarrow\)\(A< B\)
Vậy \(A< B\)
Chúc bạn học tốt ~
Ta có : A = \(\frac{10^{12345}+1}{10^{12346}+1}< 1\)
=> A < \(\frac{10^{12345}+1+9}{10^{12346}+1+9}=\frac{10^{12345}+10}{10^{12346}+10}=\frac{10^{12344}+1}{10^{12345}+1}\)= B
Vậy A < B
Tính nhanh:
a,2012.2012-2014.2010
b,1.2+2.3+3.4+...+98.99.100
c, (12345.24689-12344):(24689.12344+12345)
a) = 4048144 - 4048140 = 4
UvU
hok tốt
mik có thắc mắc dấu " . " chấm này là nhân hay phẩy vậy bạn ??
Sorry bạn nha, dấu nhân đấy
a) Ta có : 2012.2012 - 2014.2010
= 2012.2012 - (2012 + 2).(2012 - 2)
= 2012.2012 - 2012.2012 - 2.2012 + 2.2012 - 2.2
= 0 - 4
= - 4
b) Đặt A = 1.2 + 2.3 + 3.4 + ... + 98.99 + 99.100
=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 98.99.3 + 99.100.3
=> 3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 98.99.(100 - 97) + 99.100(101 - 98)
=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 98.99.100 - 97.98.99 + 99.100.101 - 98.99.100
=> 3A = 99.100.101
=> 3A = 999 900
=> A = 333 300
c) Ta có : (12345.23689 - 12344) : (24689.12344 + 12345)
\(=\frac{12345.23689-12344}{12344.23689+12345}\)
\(=\frac{\left(12344+1\right).23689-12344}{12344.23689+12345}\)
\(=\frac{12344.23689+23689-12344}{12344.23689+12345}\)
\(=\frac{12344.23689+12345}{12344.23689+12345}\)
\(=1\)