a){100:[45-45:(-9)]-32}.5-2.52
b)(25-16-32).2024
c)(34-42-2023).1280
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1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50=1275
a: \(A=3^{100}-3^{99}+3^{98}-...+3^2-3\)
=>\(3A=3^{101}-3^{100}+3^{99}-...+3^3-3^2\)
=>\(4A=3^{101}-3\)
=>\(A=\dfrac{3^{101}-3}{4}\)
b: \(B=\left(-2\right)^0+\left(-2\right)^1+...+\left(-2\right)^{2024}\)
=>\(B\cdot\left(-2\right)=\left(-2\right)^1+\left(-2\right)^2+...+\left(-2\right)^{2025}\)
=>\(-2B-B=\left(-2\right)^1+\left(-2\right)^2+...+\left(-2\right)^{2025}-\left(-2\right)^0-\left(-2\right)^1-...-\left(-2\right)^{2024}\)
=>\(-3B=-2^{2025}-1\)
=>\(B=\dfrac{2^{2025}+1}{3}\)
c: \(C=\left(-\dfrac{1}{5}\right)^0+\left(-\dfrac{1}{5}\right)^1+...+\left(-\dfrac{1}{5}\right)^{2023}\)
=>\(\left(-\dfrac{1}{5}\right)\cdot C=\left(-\dfrac{1}{5}\right)^1+\left(-\dfrac{1}{5}\right)^2+...+\left(-\dfrac{1}{5}\right)^{2024}\)
=>\(\left(-\dfrac{6}{5}\right)\cdot C=\left(-\dfrac{1}{5}\right)^{2024}-\left(-\dfrac{1}{5}\right)^0\)
=>\(C\cdot\dfrac{-6}{5}=\dfrac{1}{5^{2024}}-1=\dfrac{1-5^{2024}}{5^{2024}}\)
=>\(C\cdot\dfrac{6}{5}=\dfrac{5^{2024}-1}{5^{2024}}\)
=>\(C=\dfrac{5^{2024}-1}{5^{2024}}:\dfrac{6}{5}=\dfrac{5^{2024}-1}{6\cdot5^{2023}}\)
Các số có căn bậc hai:
a = 0 c = 1 d = 16 + 9
e = 32 + 42 h = (2-11)2 i = (-5)2
l = √16 m = 34 n = 52 - 32
Căn bậc hai không âm của các số đó là:
a ) 25 - ( - 75 ) + 32 - ( 32 + 75
= 25 + 75 + 32 - 32 - 75
= 100 + 0 - 75
= 25
b ) 24 . ( 16 - 5 ) - 16 . ( 24 - 15 )
= 24 . 11 - 16 . 9
= 264 - 144
= 120
c ) 29 . ( 19 - 13 ) - 19 - ( 29 - 13 )
29 . 6 - 19 - 29 + 13
= 174 - 19 - 29 + 13
= 126 + 13
= 139
d ) ( 55 + 45 15 ) - ( 15 - 55 + 45 )
= 4570 - 15 + 10
= 4555 + 10
= 4565
a: \(\left\{100:\left[45-45:\left(-9\right)\right]-32\right\}\cdot5-2\cdot5^2\)
\(=\left\{100:\left[45+5\right]-32\right\}\cdot5-2\cdot25\)
\(=\left\{100:50-32\right\}\cdot5-50\)
\(=\left(-30\right)\cdot5-50\)
=-150-50
=-200
b: \(\left(25-16-3^2\right)\cdot2024\)
\(=\left(9-9\right)\cdot2024\)
\(=0\cdot2024=0\)
c: \(\left(34-42-2023\right)\cdot128^0\)
\(=34-42-2023\)
=-8-2023
=-2031