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\(A=-5^{22}\left\{-222\left[-122-\left(100-5^{22}\right)+2022\right]\right\}\)
\(A=-5^{22}\left\{-222\left[1900-\left(100-5^{22}\right)\right]\right\}\)
\(A=-5^{22}\left[-222\left(1900-100+5^{22}\right)\right]\)
\(A=-5^{22}\left[-222\left(1800+5^{22}\right)\right]\)
\(A=-5^{22}\left(-399600-222\cdot5^{22}\right)\)
\(A=399600\cdot5^{22}+222\cdot5^{44}\)
Lời giải:
$=5^{22}-22+[122-(100+5^{22})+2022]$
$=5^{22}-22+122-100-5^{22}+2022$
$=(5^{22}-5^{22})+(-22+122-100)+2022$
$=0+0+2022=2022$
A = - 522 - { - 222 - [ - 122 - (100 - 522) + 2022] }
A = - 522 - { -222 - [- 122 - 100 + 522 ] + 2022}
A = - 522 - { -222 - { - 222 + 522 } + 2022}
A = - 522 - {- 222 + 222 - 522 + 2022}
A = -522 + 522 - 2022
A = - 2022
B = 1 + \(\dfrac{1}{2}\)(1 + 2) + \(\dfrac{1}{3}\).(1 + 2 + 3) + ... + \(\dfrac{1}{20}\).(1 + 2+ 3 + ... + 20)
B = 1+\(\dfrac{1}{2}\)\(\times\)(1+2)\(\times\)[(2-1):1+1]:2+ ... + \(\dfrac{1}{20}\)\(\times\) (20 + 1)\(\times\)[(20-1):1+1]:2
B = 1 + \(\dfrac{1}{2}\) \(\times\) 3 \(\times\) 2:2 + \(\dfrac{1}{3}\) \(\times\)4 \(\times\) 3 : 2+....+ \(\dfrac{1}{20}\) \(\times\)21 \(\times\) 20 : 2
B = 1 + \(\dfrac{3}{2}\) + \(\dfrac{4}{2}\) + ....+ \(\dfrac{21}{2}\)
B = \(\dfrac{2+3+4+...+21}{2}\)
B = \(\dfrac{\left(21+2\right)\left[\left(21-2\right):1+1\right]:2}{2}\)
B = \(\dfrac{23\times20:2}{2}\)
B = \(\dfrac{23\times10}{2}\)
B = 23
Lời giải:
\(=-5^{22}-(-222-(-122-100+5^{22}+2022))\)
\(=-5^{22}-(-222+122+100-5^{22}-2022)\)
\(=-5^{22}+222-122-100+5^{22}+2022\)
\(=(-5^{22}+5^{22})+222-(122+100)+2022=0+222-222+2022=2022\)
a) 5300=(53)100=125100 ; 3500=(35)100=243100 vì 125100<243100 nên 5300<3500. còn mấy cậu bạn tự làm nhé !
\(51^{51}=\overline{.....1}\)
\(99^{99}=\left(99^2\right)^{49}\cdot9=\overline{....1}^{49}\cdot9=\overline{....1}\cdot9=\overline{....9}\)
\(22^{22}=\left(22^4\right)^5\cdot2^2=\overline{...6}^5\cdot4=\overline{...6}\cdot4=\overline{....4}\)
\(222^{101}=\left(222^4\right)^2^5\cdot222=\overline{...6}^{25}\cdot222=\overline{....6}\cdot222=\overline{....2}\)
a) Ta có: 333777 = 333111.7 = (7773)111
777333 = 777111.3 = (7773)111
Vì 7773<3337 nên (7773)111 < (7773)111
Vậy 333777 > 777333
b) Ta có: 2222 = 22.111 =(2111)2
2222 = 2211.2 = (2211)2
Vì 2111 > 2211 nên (2111)2 > (2211)2
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