TÍNH C = 2100-299-298-....-2-1
Giúp vs. Thanks trc nhé
S=2100-299+298+...+22-2
giúp tớ vs aaa
tớ cảm ơn
Sửa đề: \(S=2^{100}-2^{99}+2^{98}-...+2^2-2\)
=>\(2\cdot S=2^{101}-2^{100}+2^{99}-...+2^3-2^2\)
=>\(2S+S=2^{100}-2^{99}+2^{98}-...+2^2-2+2^{101}-2^{100}+2^{99}-...+2^3-2^2\)
=>\(3S=2^{101}-2\)
=>\(S=\dfrac{2^{101}-2}{3}\)
Tính
A= 2100 - 299 - 298 - 297 - .......... - 22 - 2 - 1
\(A=2^{100}-\left(2^{99}+2^{98}+...+2+1\right)\)
Đặt \(B=2^{99}+2^{98}+...+2+1\)
\(\Rightarrow2B=2^{100}+2^{99}+...+2^2+2\)
\(\Rightarrow2B-B=2^{100}-1\Leftrightarrow B=2^{100}-1\)
\(\Rightarrow A=2^{100}-\left(2^{100}-1\right)=1\)
2100-299-298-...-2-1
2100 - 299 - 298 - ... - 2 - 1 = 2100 - ( 299 + 298 + ... + 2 + 1 )
= 2100 - { ( 299 + 1 ) . [ ( 299 - 1) : 1 + 1 ] : 2 }
= 2100 - { 300 . 299 :2 }
= 2100 - 22425
= -20325
Tính:
A=2100-299-298-...-22-2-1
Ta có: \(A=2^{100}-2^{99}-2^{98}-...-2^2-2-1\)
\(\Leftrightarrow2A=2^{101}-2^{100}-2^{99}-...-2^3-2^2-2\)
\(\Leftrightarrow2A-A=2^{101}-2^{100}-2^{99}-...-2^3-2^2-2-2^{100}+2^{99}+2^{98}+...+2^2+2+1\)
\(\Leftrightarrow A=2^{101}-2\cdot2^{100}+1\)
\(\Leftrightarrow A=1\)
a, A= 2100 - 299 - 298 - 297 - ... - 2 -
tham khảo
https://olm.vn/hoi-dap/tim-kiem?q=A=2100-299-298-297-.........-22-2-1+.+t%C3%ADnh+A&id=52301
\(A=2^{100}-2^{99}-2^{98}-...-2\)
\(\Rightarrow-2A=-2^{101}+2^{100}+2^{99}+...+2^2\)
\(\Rightarrow A-2A=2^{100}-2^{99}-...-2-2^{101}+2^{100}+...2^2\)
\(\Rightarrow-A=2^{100}+2^{100}-2^{101}-2\)
\(\Rightarrow-A=-2\Rightarrow A=2\)
Thu gọn
2100-299-298-...-2-1
\(A=2^{100}-2^{99}-...-1\)
\(\Rightarrow2A=2^{101}-2^{100}-...-2\)
\(\Rightarrow2A+A=2^{101}-2^{100}-...-2+2^{100}+2^{99}+1\)
\(\Rightarrow3A=2^{101}-1\)
\(\Rightarrow A=\dfrac{2^{101}-1}{3}\)
A=2100-299+298-297+...-23+22-2+1
HELP ME
\(A=2^{100}-2^{99}+2^{98}-2^{97}+....-2^3+2^2-2+1\\ A=\left(2^{100}+2^{98}+...+2\right)-\left(2^{99}+2^{97}+...+1\right)\)
Gọi \(\left(2^{100}+2^{98}+...+2\right)\)là B
\(B=\left(2^{100}+2^{98}+...+2\right)\\ 2B=2^{102}+2^{100}+.....+2^2\\ 2B-B=\left(2^{102}+2^{100}+.....+2^2\right)-\left(2^{100}+2^{98}+...+2\right)\\ B=2^{102}-2\)
Gọi \(\left(2^{99}+2^{97}+...+1\right)\) là C
\(C=\left(2^{99}+2^{97}+...+1\right)\\ 2C=2^{101}+2^{99}+....+2\\ 2C-C=\left(2^{101}+2^{99}+9^{97}+...+2\right)-\left(2^{99}+9^{97}+...+1\right)\\ C=2^{101}-1\)
\(A=B+C\\ =>A=2^{102}-2+2^{101}-1\\ A=2^{101}\left(2+1\right)-3\\ A=2^{101}\cdot3-3\\ A=3\cdot\left(2^{101}-1\right)\)
\(\dfrac{1}{2}A=2^{99}-2^{98}+...-1+\dfrac{1}{2}\\ \Rightarrow A-\dfrac{1}{2}A=2^{100}-\dfrac{1}{2}\\ \Rightarrow A=2^{101}-1\)
CMR :
2100 - 299 + 298 - 297 + ...... + 24 - 23 + 22 ⋮ 12
\(2^{100}-2^{99}+2^{98}-2^{97}+2^{96}-2^{95}+...+2^4-2^3+2^2\)
\(=\left(2^{100}-2^{99}+2^{98}\right)-\left(2^{97}-2^{96}+2^{95}\right)+...+\left(2^4-2^3+2^2\right)\)
\(=2^{96}\left(2^4-2^3+2^2\right)-2^{93}\left(2^4-2^3+2^2\right)+...+\left(2^4-2^3+2^2\right)\)
\(=12\left(2^{96}-2^{93}+...+1\right)⋮12\)
a, A = 1 + 2 + 22 + 23 + ... + 250 =
b, B = 1 + 3 + 32 + 33 + ... 3100 =
c, C = 5 + 52 + 53 + ... 530 =
d, D = 2100 = 299 + 298 - 297 + ... + 22 - 2
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) \(D=2^{100}-2^{99}+2^{98}-...+2^2-2\)
\(\Rightarrow2D=2^{101}-2^{100}+2^{99}-...+2^3-2^2\)
\(\Rightarrow3D=2D+D=2^{101}-2^{100}+2^{99}-...+2^3-2^2+2^{100}-2^{99}+...+2^2-2=2^{101}-2\)
\(\Rightarrow D=\dfrac{2^{101}-2}{3}\)