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a) \(A=1+2+2^2+...+2^{50}\)
\(\Rightarrow2A=2+2^2+...+2^{51}\)
\(\Rightarrow A=2A-A=2+2^2+...+2^{51}-1-2-2^2-...-2^{50}=2^{51}-1\)
b) \(B=1+3+3^2+...+3^{100}\)
\(\Rightarrow3B=3+3^2+...+3^{101}\)
\(\Rightarrow2B=3B-B=3+3^2+...+3^{101}-1-3-3^2-...-3^{100}=3^{101}-1\)
\(\Rightarrow B=\dfrac{3^{101}-1}{2}\)
c) \(C=5+5^2+...+5^{30}\)
\(\Rightarrow5C=5^2+5^3+...+5^{31}\)
\(\Rightarrow4C=5C-C=5^2+5^3+...+5^{31}-5-5^2-...-5^{30}=5^{31}-5\)
\(\Rightarrow C=\dfrac{5^{31}-5}{4}\)
d) \(D=2^{100}-2^{99}+2^{98}-...+2^2-2\)
\(\Rightarrow2D=2^{101}-2^{100}+2^{99}-...+2^3-2^2\)
\(\Rightarrow3D=2D+D=2^{101}-2^{100}+2^{99}-...+2^3-2^2+2^{100}-2^{99}+...+2^2-2=2^{101}-2\)
\(\Rightarrow D=\dfrac{2^{101}-2}{3}\)
a, 34.275.(32)3 = 34.(33)5.36 = 34.315.36 = 325
b, (23)4.46.32 = 212.212.25 = 229
c, 32019.62019: 22019 = 32019.32019.22019:22019 = (3.3)2019= 92019
d, 1258.(52)4 = (53)8.58 = 532
a. (15+37)+(52-37-17) = 15+37+52-37-17
= 15+(37-37)+52-17
= 15+0+35
= 50
\(A=2+2^2+...+2^{20}\)
\(2A=2^2+2^3+...+2^{21}\)
\(2A-A=2^2+2^3+...+2^{21}-2-2^2-...-2^{20}\)
\(A=2^{21}-2\)
___________
\(B=5+5^2+...+5^{50}\)
\(5B=5^2+5^3+...+5^{51}\)
\(5B-B=5^2+5^3+...+5^{51}-5-5^2-...-5^{50}\)
\(4B=5^{51}-5\)
\(B=\dfrac{5^{51}-5}{4}\)
___________
\(C=1+3+3^2+...+3^{100}\)
\(3C=3+3^2+...+3^{101}\)
\(3C-C=3+3^2+...+3^{101}-1-3-3^2-...-3^{100}\)
\(2C=3^{101}-1\)
\(C=\dfrac{3^{101}-1}{2}\)
3 câu đầu bn Võ Quang Huy lm đúng nhưng câu cuối là bằng -22 nhé bn
a)\(...A=\dfrac{2^{50+1}-1}{2-1}=2^{51}-1\)
b) \(...\Rightarrow B=\dfrac{3^{80+1}-1}{3-1}=\dfrac{3^{81}-1}{2}\)
c) \(...\Rightarrow C+1=1+4+4^2+4^3+...+4^{49}\)
\(\Rightarrow C+1=\dfrac{4^{49+1}-1}{4-1}=\dfrac{4^{50}-1}{3}\)
\(\Rightarrow C=\dfrac{4^{50}-1}{3}-1=\dfrac{4^{50}-4}{3}=\dfrac{4\left(4^{49}-1\right)}{3}\)
Tương tự câu d,e,f bạn tự làm nhé
a) ( 15 + 37 ) + ( 52 - 37 - 17 )
= 15 + 37 + 52 - 37 - 17
= 50
b) ( 38 + 42 + 14 ) - ( 25 - 27 - 15 )
= 38 + 42 + 14 - 25 + 27 + 15
= 111
c) - (21 - 32 ) - ( - 12 + 32 )
= - 21 + 32 + 12 - 32
= - 9
d) - ( 12 + 21 - 23 ) - ( 23 - 21 + 10 )
= - 12 - 21 + 23 - 23 + 21 - 10
= - 22
Trả lời:
a,(15+37) + (52-37-17)
=15+37+52-37-17
=(15+52-17)+(37-37)
=50+0
=50
b,(38+42+14)-(25-27-15)
=38-42+14-25+27+15
=(38+14-42)-(25-25)+27
=10-0+27
=37
c,-(21-32)-(-12+32)
=-21+32+12-32
= -(21+12)+(32-32)
= -9+0
=-9
d,-(12+21-23)-(23-21+10)
= -12-21+23-23+21+10
=(-12+10)-(21-21)-(23-23)
= -2-0+0
= -2
b
Chọn B