A = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + 2^10 B = 1 + 3 + 3^2 + 3^3 + 3^4 + ... + 3^100.
Tính:
a) -5/7(14/5 - 7/10) : |-2/3| - 3/4(8/9 + 16/3) + 10/3(1/3 + 1/5)
b) 17/-26(1/6 - 5/3) : 17/13 - 20/3(2/5 - 1/4) + 2/3(6/5 - 9/2)
c) -8/9(9/8 - 3/2) + 5/4 : (5/2 - 15/4) - 3/4(10/9 - 8/3) : (-1/3)
d) 21/10 : (12/5 - 9/10) . (-4/7) - 3/2(1/6 - 7/12) + 1/5(3/2 - 1/4)
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
1) Thuc hien phep tinh:
a) 4^6 × 9^2 / 6^3 × 8^2
b) 5^6 × 15^4 /5^4 × 3^3
c) 3^9 - 2^3 × 3^7 + 2^10 × 3^2 - 2^13 / 3^10 - 2^2 × 3^7 + 2^10 × 3^3 - 2^12
d) (1/9)^10 : (1/3)^20
e) (1/64)^5 × (1/4)^7
2) Chung minh rang:
a)2014^100+2014^99 chia het cho 2015
b) 4^13+32^5-8^8 chia het cho 5
c) 81^27-27^9-9^13 chia het cho 405
Help me!! Pleass!!
tính các tổng sau
1) A = 1+7+7^2+7^3+....+7^2007
2) B= 1+4 +4^2+4^3+....+4^100
3) C= 1+3^2 +3^4 +3^6+3^8+....+3^100
4) D= 7+7^3 + 7^5+7^7+7^9+....+7^99
5)E= 2+2^3+2^5+2^7+2^9+....+2^2009
6) B = 1+2^2+2^4+2^6+2^8+....+2^200
7) C= 5+5^3+5^5+5^9+....+5^101
8) D = 13+13^3+13^5+...+13^99
Mình làm mẫu 1 bài rùi bạn tự giải những bài còn lại nha
1, 7A = 7+7^2+7^3+....+7^2008
6A = 7A - A = (7+7^2+7^3+....+7^2008)-(1+7+7^2+....+7^2007) = 7^2008-1
=> A = (7^2008-1)/6
Tk mk nha
\(A=1+7+7^2+7^3+...+7^{2007}\)
\(\Rightarrow7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(\Rightarrow7A-A=\left(7+7^2+7^3+...+7^{2008}\right)-\left(1+7+7^2+...+7^{2007}\right)\)
\(\Rightarrow6A=7^{2008}-1\)
\(\Rightarrow A=\frac{7^{2008}-1}{6}\)
4b=4+4^2+4^3+...+4^101
4b-b=(4+4^2+...+4^101)-(1+4+4^2+...+4^100)
3b=4^101-1
b=(4^101-1):3
Bài 3: Tính
1 + 5 =
2 + 3 =
3 + 6 =
4 + 5 =
5 + 1 =
6 + 2 =
7 + 1 =
8 + 1 =
9 + 0 =
10 + 2=
11 + 2 =
1 + 3 =
2 + 6 =
3 + 7 =
4 + 2 =
5 + 2 =
6 + 3 =
7 + 3 =
8 + 2 =
9 + 1 =
10 + 0 =
11 + 3 =
1 + 4 =
2 + 8 =
3 + 2 =
4 + 1 =
5 + 4 =
6 + 4 =
7 + 2 =
8 + 0 =
9 + 2 =
10 + 6 =
11 + 6 =
Bài 4: Tính
6 - 2 =
3 - 1 =
4 - 2 =
5 - 2 =
8 - 5 =
10 - 6 =
4 - 3 =
3 - 3 =
5 - 1 =
2 - 2 =
3 - 1 =
4 - 1 =
2 - 1 =
4 - 3 =
5 - 0 =
9 - 4 =
8 - 6 =
7 - 3 =
8 - 4 =
7 - 6 =
9 - 5 =
7 - 7=
5 - 3 =
5 - 3=
6 - 3 =
7 - 3 =
7 - 6 =
6 - 5 =
9 - 7 =
9 - 3 =
8 - 8 =
8 - 0 =
5 - 3 =
Bài 5: Tính
6 - 2 =
5 + 2 =
9 - 5 =
2 + 0 =
8 + 2 =
4 - 4 =
7 - 3 =
3 + 6 =
7 + 2 =
9 - 5 =
3 + 6 =
1 + 5 =
7 - 6 =
7 + 1 =
3 + 5 =
2 - 1 =
6 + 3 =
5 + 2 =
9 - 4 =
6 + 4 =
4 + 2 =
6 + 1=
7 - 7=
4 + 3 =
7 + 3 =
5 - 2 =
6 - 5 =
8 - 6 =
6 - 4 =
7 - 3 =
10 + 0 =
5 +4 =
8 - 2 =
1+(-2)+3+(-4)+5+(-6)+7+(-8)+9+(-10)+11+(-12)=
-1+2+(-3)+4+(-5)+6+(-7)+8+(-9)+10+(-11)+12=
(-1)+(-2)+(-3)+(-4)+.......+(-99)+(-100)=
(-1)+2+(-3)+4+.......+(-99)+100=
1+(-2)+3+(-4)+........+99+(-100)=
lam la co tick nha
1+(-2)+3+(-4)+5+(-6)+7+(-8)+9+(-10)+11+(-12)
=(1+3+5+7+9+11)+[(-2)+(-4)+(-6)+(-8)+(-10)+(-12)]
= 36+-42
=-6
(-1)+2+(-3)+4+(-5)+6+(-7)+8+(-9)+10+(-11)+12
=[(-1)+(-3)+(-5)+(-7)+(-9)+(-11)]+(2+4+6+8+10+12)
=(-36)+42
=6
Tính:
A=1+7+7^2 +7^3+..+7^2007
B=1+4+4^2+4^3+...+4^100
C=1+3^2+3^4+3^6+3^8+...+3^100
D=7+7^3+7^5+7^7+7^9+...+7^99
E=2+2^3+2^5+2^7+2^9+...+2^9009
\(A=1+7+7^2+7^3+...+7^{2007}\)
\(7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(7A-A=\left(7+7^2+7^3+7^4+...+7^{2008}\right)-\left(1+7+7^2+7^3+...+7^{2007}\right)\)
\(6A=7^{2008}-1\)
\(A=\frac{7^{2008}-1}{6}\)
Tương tự, \(B=\frac{4^{101}-1}{3},C=\frac{3^{101}-1}{2}\).
\(D=7+7^3+7^5+7^7+...+7^{99}\)
\(7^2.D=7^3+7^5+7^7+7^9+...+7^{101}\)
\(\left(7^2-1\right)D=\left(7^3+7^5+7^7+7^9+...+7^{101}\right)-\left(7+7^3+7^5+7^7+...+7^{99}\right)\)
\(48D=7^{101}-7\)
\(D=\frac{7^{101}-7}{48}\)
Tương tự, \(E=\frac{2^{9011}-2}{3}\)
5) (3-1/4+2/3) - (5-1/3-6/5) - (6-7/4+3/2) 6) (6-2/3+1/2) - (5+5/3-3/2)-(3-7/3+5/2)
7) (5/3-3/7+9)-(2+5/7-2/3)+(8/7-4/3-10) 8) (8-9/4+2/7)-(-6-3/7+5/4)-(3+2/4-9/7 pls help me
5: \(=3-\dfrac{1}{4}+\dfrac{2}{3}-5+\dfrac{1}{3}+\dfrac{6}{5}-6+\dfrac{7}{4}-\dfrac{3}{2}\)
\(=3-5-6+\dfrac{-1}{4}+\dfrac{7}{4}+\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{6}{5}-\dfrac{3}{2}\)
\(=-8+\dfrac{3}{2}+1+\dfrac{-3}{10}\)
\(=-7+\dfrac{15-3}{10}=-7+\dfrac{6}{5}=-\dfrac{29}{5}\)
6: \(=6-\dfrac{2}{3}+\dfrac{1}{2}-5-\dfrac{5}{3}+\dfrac{3}{2}-3+\dfrac{7}{3}-\dfrac{5}{2}\)
\(=6-5-3-\dfrac{2}{3}-\dfrac{5}{3}+\dfrac{7}{3}+\dfrac{1}{2}+\dfrac{3}{2}-\dfrac{5}{2}\)
\(=-2-\dfrac{1}{2}=-\dfrac{5}{2}\)
7: \(=\dfrac{5}{3}-\dfrac{3}{7}+9-2-\dfrac{5}{7}+\dfrac{2}{3}+\dfrac{8}{7}-\dfrac{4}{3}-10\)
\(=9-2-10+\dfrac{5}{3}+\dfrac{2}{3}-\dfrac{4}{3}+\dfrac{-3}{7}-\dfrac{5}{7}+\dfrac{8}{7}\)
=-3+1
=-2
8: \(=8-\dfrac{9}{4}+\dfrac{2}{7}+6+\dfrac{3}{7}-\dfrac{5}{4}-3-\dfrac{2}{4}+\dfrac{9}{7}\)
\(=8+6-3+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{9}{7}-1-\dfrac{2}{4}\)
\(=11+2-1-\dfrac{1}{2}\)
=11+1/2
=11,5
Tính
b)
4 + 5 - 7 = 6 - 4 + 8 = 10 - 9 + 6 = 9 - 4 - 3 =
1 + 2 + 6 = 3 + 2 + 4 = 8 - 2 + 4 = 8 - 4 + 3 =
3 - 2 + 9 = 7 - 5 + 3 = 3 + 5 - 6 = 2 + 5 - 4 =
b) Tính theo thứ tự từ trái sang phải.
4 + 5 - 7 = 2 6 - 4 + 8 = 10 10 - 9 + 6 = 7 9 - 4 - 3 = 2
1 + 2 + 6 = 9 3 + 2 + 4 = 9 8 - 2 + 4 = 10 8 - 4 + 3 = 7
3 - 2 + 9 = 10 7 - 5 + 3 = 5 3 + 5 - 6 = 2 2 + 5 - 4 = 3
(3-1/4+2/3) - (5-1/3-6/5) - (6-7/4+3/2) (6-2/3+1/2) - (5+5/3-3/2)-(3-7/3+5/2)
(5/3-3/7+9)-(2+5/7-2/3)+(8/7-4/3-10) (8-9/4+2/7)-(-6-3/7+5/4)-(3+2/4-9/7 )
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