Cho 31. − 18 + 31. − 81 − 31 = ? Chọn đáp án đúng
A. -3100
B. 3100
C. 0
D. 31
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\(B=3^0+3^1+3^2...+3^{100}\)
\(=3^0\times\left(1+3^1+3^2\right)+3^3\times\left(1+3^1+3^2\right)+...+3^{98}\times\left(1+3^1+3^2\right)\)
\(=3^0\times13+3^3\times13+...+3^{98}\times13\)
\(=13\times\left(3^0+3^3+...+3^{98}\right)⋮13\)
Đặt A = 3¹ + 3² + 3³ + 3⁴ + ... + 3⁹⁹ + 3¹⁰⁰
= (3¹ + 3²) + (3³ + 3⁴) + ... + (3⁹⁹ + 3¹⁰⁰)
= 3.(1 + 3) + 3³.(1 + 3) + ... + 3⁹⁹.(1 + 3)
= 3.4 + 3³.4 + ... + 3⁹⁹.4
= 4.(3 + 3³ + ... + 3⁹⁹) ⋮ 4
Vậy A ⋮ 4
B = 31 + 32 + 33 +...+ 3100
3B = 32 + 33 + ...+ 3100 + 3101
3B - B = 3101 - 3
2B = 3101 - 3
2B + 3 = 3n
⇒ 3101 - 3 + 3= 3n
3n = 3101
n = 101
Kết luận n = 101
Sửa đề: \(C=1+3^1+3^2+...+3^{100}\)
b) Ta có: \(C=1+3^1+3^2+...+3^{100}\)
\(\Leftrightarrow3\cdot C=3+3^2+...+3^{101}\)
\(\Leftrightarrow C-3\cdot C=1+3+3^2+...+3^{100}-3-3^2-...-3^{100}-3^{101}\)
\(\Leftrightarrow-2\cdot C=1-3^{101}\)
hay \(C=\dfrac{3^{101}-1}{2}\)
b) Ta có: C=1+31+32+...+3100C=1+31+32+...+3100
⇔3⋅C=3+32+...+3101⇔3⋅C=3+32+...+3101
⇔C−3⋅C=1+3+32+...+3100−3−32−...−3100−3101⇔C−3⋅C=1+3+32+...+3100−3−32−...−3100−3101
⇔−2⋅C=1−3101
\(B=3^1+3^2+3^3+...+3^{100}\\3B=3^2+3^3+3^4+...+3^{101}\\3B-B=(3^2+3^3+3^4+...+3^{101})-(3^1+3^2+3^3+...+3^{100})\\2B=3^{101}-3\\\Rightarrow 2B+3=3^{101}\)
Mặt khác: \(2B+3=3^n\)
\(\Rightarrow 3^n=3^{101}\\\Rightarrow n=101(tm)\)
Vậy n = 101.
a)29 . (19 – 13) – 19 . (29 – 13)
= 29 . 6 – 19 . 16
= 174 – 304
= –130.
b)31.(-18)+31.(-81)-31
= 31. [-18 + (-81) - 1 ]
= 31. (-100)
= -3100
c)(7.3-3):(-6)
(7.3-3):(-6)
= (21-3):(-6)
= 18 : (-6)
= 3
d)72:[(-6).2+4)]
= 72 : ( -12 + 4 )
= 72 : -8
= -9
31 than -> to
32 less -> fewer
33 go -> went
34 on -> at
35 in -> on
36 city -> cities
37 hardly -> hard
38 more -> most
39 houseworks -> housework
40 too -> either
Mỗi câu sau trong 4 đáp án A, B , C , D có 1 lỗi sai . Hãy tìm và sửa lại cho đúng.
31. Many people prefer taking part in sports than=>to watching them.
A B C D
32. My father has less=>fewer days off than Tim’s father.
A B C D
33. Three days ago, The Browns go=>went for a picnic in the country.
A B C D
34. You look tired. You’d better stay inside on=>at recess.
A B C D
35. We have English classes in=>on Monday, Wednesday and Friday.
A B C D
36. Da Nang is one of the biggest city=>cities in Viet Nam.
A B C D
37. Nga is a keen student and she studies very hardly=>hard before tests.
A B C D
38. Tuan is the more=>most intelligent student in our class.
A B C D
39.My father always has a lot of houseworks=>housework to do.
A B C D
40. My brother doesn't like durians, and I don't like them, too=>either.
A B C D
Chọn A
31. − 18 + 31. − 81 − 31 = 31. − 18 + 31. − 81 − 31.1 = 31. − 18 + − 81 − 1 = 31. − 100 = − 3100
bằng A