a) Ta có: \(A=1+2013+2013^2+...+2013^{99}\)

   \(2013A=2013+2013^2+2013^3+...+2013^{100}\)

\(2013A-A=2013^{100}-1\)

Hay \(2012A=2013^{100}-1\)

\(\Rightarrow2012A=2013^{100}-1< 2013^{100}=B\)

\(\Rightarrow A< B\)

_Học tốt_

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Ta có:

\(9^{12}=\left(9^6\right)^2=531441^2\)

\(26^2=26^2\)

Vì 531441 > 26 nên 9^12>26^2

9¹² = ( 9⁶ )²

26² = 26²

9⁶ = 531441

Mà 531441 > 26 nên 9¹² > 26² 

9¹²= (9⁶)² = 531441²

Vì 531441> 26=> 531441²> 26²

Vậy 9¹² > 26²

a) \(27^{15}=\left(3^3\right)^{15}=3^{45}\)

\(81^{11}=\left(3^4\right)^{11}=3^{44}\)

vì 3⁴⁴ < 3⁴⁵ nên 81¹¹ < 27¹⁵

27¹⁵ = (3³)¹⁵ = 3⁴⁵

81¹¹ = (3⁴)¹¹ = 3⁴⁴

Vì 3⁴⁵ > 3⁴⁴ nên 27¹⁵ > 81¹¹

ta có: 3^99=(3^3)^33=27^33 > 11^21

\(\Rightarrow\)3^99>11^21

b) 7/9

\(\text{a)}\dfrac{3}{4}+\dfrac{2}{5}\)

\(=\dfrac{15}{20}+\dfrac{8}{20}=\dfrac{23}{20}\)

\(\text{b)}\dfrac{5}{17}+\dfrac{2}{3}-\dfrac{5}{3}+\dfrac{7}{9}+\dfrac{12}{17}\)

\(=\dfrac{5}{17}+\dfrac{2}{3}+\left(\dfrac{-5}{3}\right)+\dfrac{7}{9}+\dfrac{12}{17}\)

\(=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)+\left[\dfrac{2}{3}+\left(\dfrac{-5}{3}\right)\right]+\dfrac{7}{9}\)

\(=1+\left(-1\right)+\dfrac{7}{9}\)

\(=0+\dfrac{7}{9}=\dfrac{7}{9}\)

\(a,\dfrac{3}{4}+\dfrac{2}{5}\)

\(=\dfrac{15}{20}+\dfrac{8}{20}\)

\(=\dfrac{23}{20}\)

b,

\(5^4< 4^5\)

a.Ta có:

  5⁴=5x5x5x5=625

  4⁵=4x4x4x4=256

625 > 256 => 5⁴ > 4⁵

Ta có: 5^4=3125;4^5=1024

Do 3125>1024 nên 5^4>4^5