Tính nhanh nếu có thể :
a ) 72 . 37 - 9 . 22 . 8 + 18 . 4 . 85
b ) { 149 - [ 2 . ( 10 . 3 2 - 5 2 . 2 ) - 44 ] + 2 3 } : 11 2
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a: \(=\dfrac{-39+19+10}{12}=\dfrac{-10}{12}=\dfrac{-5}{6}\)
b: \(=\dfrac{2^{30}\cdot3^{16}\cdot7-2^{34}\cdot3^{15}}{2^{28}\cdot3^{21}-2^{28}\cdot3^{17}}\)
\(=\dfrac{2^{30}\cdot3^{15}\left(3\cdot7-2^4\right)}{2^{28}\cdot3^{17}\left(3^4-1\right)}=\dfrac{2^2}{3^2}\cdot\dfrac{21-16}{80}=\dfrac{4}{9}\cdot\dfrac{5}{80}\)
\(=\dfrac{20}{720}=\dfrac{1}{36}\)
a: =-5/9-4/9+8/15+7/15-2/11=-2/11
b: =10/17+7/17-5/13-8/13+11/25
=11/25
c: =(9/12-2/12)*3/2=7/12*3/2=21/24=7/8
d: =(31/10-25/10)*3-2
=3/5*3-2
=9/5-2
=-1/5
A = 1 + 2 + 2² + 2³ + ... + 2²⁰²³
⇒ 2A = 2 + 2² + 2³ + 2⁴ + ... + 2²⁰²⁴
⇒ A = 2A - A
= (2 + 2² + 2³ + 2⁴ + ... + 2²⁰²⁴) - (1 + 2 + 2² + 2³ + ... + 2²⁰²³)
= 2²⁰²⁴ - 1
\(A=1+2+2^2+...+2^{2023}\)
\(2\cdot A=2\cdot\left(1+2+2^2+...+2^{2023}\right)\)
\(2A=2+2^2+2^3+....+2^{2024}\)
\(2A-A=\left(2+2^2+...+2^{2024}\right)-\left(1+2+2^2+...+2^{2023}\right)\)
\(A=2+2^2+2^3+....+2^{2024}-1-2-2^2-...-2^{2023}\)
\(A=2^{2024}-1\)
a, Số các số hạng của dãy là :
( 175 - 1 ) : 2 + 1 = 88 ( số hạng )
Tổng dãy là :
( 175 + 1 ).88 : 2 = 7744
Đáp số : 7744
các câu sau tương tự nhé
Học tốt
a) \(1+3+5+7+...+173+175\)
\(\Rightarrow\frac{\left(175+1\right)\left[\left(175-1\right):2+1\right]}{2}=7744\)
b) \(6+8+10+12+...+170\)
\(\Rightarrow\frac{\left(170+6\right)\left[\left(170-1\right):2+1\right]}{2}=7524\)
c)\(2+5+8+11+...+200\)
\(\Rightarrow\frac{\left(200+2\right)\left[\left(200-2\right):3+1\right]}{2}=6767\)
d)\(4+7+10+13+...+400\)
\(\Rightarrow\frac{\left(400+4\right)\left[\left(400-4\right):3+1\right]}{2}=26866\)
e)\(1+5+9+...+401\)
\(\Rightarrow\frac{\left(401+1\right)\left[\left(401-1\right):4+1\right]}{2}=20301\)
g)\(1+6+11+16+...+566\)
\(\Rightarrow\frac{\left(566+1\right)\left[\left(566-1\right):5+1\right]}{2}=32319\)
\(\dfrac{-1}{9}.\dfrac{-3}{5}+\dfrac{5}{-6}.\dfrac{-3}{5}-\dfrac{7}{2}.\dfrac{3}{5}\)
\(=\dfrac{3}{5}.\left(\dfrac{1}{9}+\dfrac{5}{6}-\dfrac{7}{2}\right)\)
\(=\dfrac{3}{5}.\left(\dfrac{2}{18}+\dfrac{15}{18}-\dfrac{63}{18}\right)\)
\(=\dfrac{3}{5}.\left(-\dfrac{23}{9}\right)\)
\(=-\dfrac{69}{45}\)
\(a.10-\left[12-\left(-9-1\right)\right]\)
\(=10-12+9+1\)
\(=8\)
\(a,10-\left[12-\left(-9-1\right)\right]\)
\(=10-\left[12+9+1\right]\)
\(=10-22=-12\)
\(b,271-\left[\left(-43\right)+27-\left(-17\right)\right]\)
\(=271-\left[-43+27+17\right]\)
\(=271-\left[1\right]\)
\(=270\)
\(c,-144-\left[29-144-144\right]\)
\(=-144-29+144+144\)
\(=144-29=115\)
\(2^{x+3}.2=2^2.3+52\)
\(=>2^{x+3}.2=64\)
\(=>2^{x+3}=64:2\)
\(=>2^{x+3}=32\)
\(=>2^{x+3}=2^5\)
=>x+3=5
=>x=5-3
=>x=2
Vậy ...........
2x + 3 . 2 = 22 . 3 + 52
2x + 3 . 2 = 4 . 3 + 52
2x + 3 . 2 = 12 + 52
2x + 3 . 2 = 64
2x + 3 = 64 : 2
2x + 3 = 32
2x + 3 = 25
x + 3 = 5
x = 5 - 3
x = 2
Vậy x = 2
a ) 72 . 37 - 9 . 22 . 8 + 18 . 4 . 85
= 72 . 37 - 72 . 22 + 72 . 85
= 72 . ( 37 - 22 + 85 )
= 72 . 100
= 7200
b ) { 149 - [ 2 . ( 10 . 3 2 - 5 2 . 2 ) - 44 ] + 2 3 } : 11 2
= { 149 - [ 2 . 40 - 44 ] + 8 } : 121
= { 149 - 36 + 8 } : 121
= 121 : 121
= 1