Cho A = 13 + 132 + 133 + 134 + 135 + 136. Chứng tỏ rằng A ⋮ 2
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ENGLISH ON TAG QUESTION
131. They don't like cats, ____do they____?
132. She loves flowers, ____doesn't she____?
133. You are a student, ___aren't you____?
134. Jane can't swim, _____can she___?
135. They mustn't buy the car, ____must they____?
136. Billy has made a beautiful kite, ____hasn't he____?
137. You won't trust him, ____will you___?
138. Kathy and YoYo will go to the swimming pool tomorrow, ____won't they____?
139. Mrs. White ate a lot of fish yesterday, ____didn't she____?
140. Ken didn't visit his grandfather last week, ___did he____?
141. You don't like fishing, _____do you___?
142. Fiona likes Jacky Chan, ____doesn't she____?
143. She must come to the party, ___mustn't she____?
144. Lucy will buy the dress, ___won't she_____?
145. Mimi and Lily were sad yesterday, ____weren't they____?
146. Kate always sleeps early, ____doesn't she____?
147. He won't be happy, ___will he____?
148. You didn't do homework yesterday, ___did you____?
149. We kept some money under the bed, ____didn't we____?
150. It seldom barks, ___does it_____?
151. Michael and Melody often go home late, ____don't they____?
152. Hugh had a red car, ___didn't he_____?
153. The Mount Rushmore National Memorial Park is in Keystone, ____isn't it___?
154. The rock was a sacred Indian site once, ___wasn't it____?
155. It has been a national memorial since 1925, ____hasn't it___?
156. The monument doesn't show the bust of President Clinton, ____does it___?
157. George Washington was the first President of the United States, ____wasn't he___?
158. Mr. McGuinness is from Ireland, ____isn't he___?
159. The car isn't in the garage, ___is it____?
160. You are John, ___aren't you____?
161. She went to the library yesterday, ___didn't she____?
Các số không chia hết cho 3 nhưng không chia hết cho 9 là: 132
Các số vừa không chia hết cho 3 và vừa không chia hết cho 9 là: 133; 134; 143; 145
c: \(S=13+13^2+13^3+\cdots+13^{2022}\)
=>\(13S=13^2+13^3+\cdots+13^{2023}\)
=>13S-S=\(13^2+13^3+\cdots+13^{2023}-13-13^2-\cdots-13^{2022}\)
=>12S=\(13^{2023}-13\)
=>12S+13=\(13^{2023}\)
=>\(13^{2x+1}=13^{2023}\)
=>2x+1=2023
=>2x=2022
=>x=1011
d: \(S=13+13^2+13^3+\cdots+13^{2022}\)
\(=\left(13+13^2\right)+\left(13^3+13^4\right)+\cdots+\left(13^{2021}+13^{2022}\right)\)
\(=13\left(1+13\right)+13^3\left(1+13\right)+\cdots+13^{2021}\left(1+13\right)=14\left(13+13^3+\cdots+13^{2021}\right)\) ⋮14
b: Ta có: \(S=13+13^2+\cdots+13^{2022}\)
\(=\left(13+13^2\right)+\left(13^3+13^4+13^5+13^6\right)+\left(13^7+13^8+13^9+13^{10}\right)+\cdots+\left(13^{2019}+13^{2020}+13^{2021}+13^{2022}\right)\)
\(=\left(13+169\right)+13^3\left(1+13+13^2+13^3\right)+13^7\left(1+13+13^2+13^3\right)+\cdots+13^{2019}\left(1+13+13^2+13^3\right)\)
\(=182+\left(1+13+13^2+13^3\right)\left(13^3+13^7+\cdots+13^{2019}\right)\)
\(=2+180+2380\left(13^3+13^7+\cdots+13^{2019}\right)\)
=>S chia 10 dư 2
=>S có tận cùng là 2
A = 13 + 132 + 133 + 134 + 135 + 136
A = (13 + 132) + ( 133 + 134) + (135 + 136)
A = 13 \(\times\) ( 1 + 13) + 133 \(\times\) ( 1 + 13) + 135 \(\times\) ( 1 + 13)
A = 13 \(\times\) 14 + 133 \(\times\) 14 + 135 \(\times\) 14
A = 14 \(\times\) ( 13 + 133 + 135) vì 14 ⋮ 2
⇒ A ⋮ 2 ( đpcm)