55⁶⁶>66⁵⁵

55⁶⁶>66⁵⁵. like ik ha.^-^

Ta có:    55^66 = (55^6)^11 = ((11.5)^6)^11 = (11^6.5^6)^11 = (11^5.11.5^6)^11

              66^55 = (66^5)^11 = ((11.6)^5)^11 = (11^5.6^5)^11

Vì 11.5^6 > 6^5 nên 55^66 > 66^55

\(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{66}\)

\(\frac{A}{2}=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{132}\)

\(\frac{A}{2}=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{11\cdot12}\)

\(\frac{A}{2}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)

\(\frac{A}{2}=\frac{1}{4}-\frac{1}{12}\)

\(\Rightarrow A=\frac{2}{4}-\frac{2}{12}=\frac{16}{48}\)

\(B=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{55}\)

\(\frac{B}{2}=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{110}\)

\(\frac{B}{2}=\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{10\cdot11}\)

\(\frac{B}{2}=\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\)

\(\frac{B}{2}=\frac{1}{3}-\frac{1}{11}\)

\(\Rightarrow B=\frac{2}{3}-\frac{2}{11}=\frac{16}{33}\)

Mà \(\frac{16}{48}< \frac{16}{33}\Rightarrow A< B\)

Vậy : A < B

15 + 25 + 35 + 45 + 55 + 65 + 75 + 85 + 95 =495 vì 495 < 500 nên 15 + 25 + 35 + 45 + 55 + 65 + 75 + 85 + 95 < 500

15 + 25 + 35 + 45 + 55 + 65 + 75 + 85 + 95 = 495

vậy 15 + 25 + 35 + 45 + 55 + 65 + 75 + 85 + 95 < 500

15 + 25 + 35 + 45 + 55 + 65 + 75 + 85 + 95 = 495.

Vậy 495 < 500

.Nhớ k cho mình nha!

\(44^{55}=\left(44^5\right)^{11}=\left(4^5.11^5\right)^{11}\)

\(55^{44}=\left(55^4\right)^{11}=\left(5^4.11^4\right)^{11}\)

mà \(11^5>11^4\) và \(4^5>5^4\)

=>\(\left(4^5.11^5\right)^{11}>\left(5^4.11^4\right)^{11}\)

=>\(44^{55}>55^{44}\)

44^55<55⁴⁴

nhớ k cho mình nha

44\(^{55}\).>55\(^{44}\)

=\(55^{6x11}và66^{5x11}\)

=\(330^{11}va330^{11}\)

=>\(55^{66}=66^{55}\)

+)  \(1+frac{-54}{55}=\frac{1}{55}\)

\(1+frac{-55}{56}=\frac{1}{56}\)

Vì: 55<56

Nên: \frac{1}{55}\)>\frac{1}{56}\)

Vậy: \frac{-54}{55}\)>\frac{-55}{56}\)

+)   \(1-frac{323232}{333333}=\frac{1}{33}\)

 \(1-frac{33333333}{34343434}=\frac{1}{34}\)

Vì: 33<34

Nên: \frac{1}{33}\)>\frac{1}{34}\)

Vậy: \frac{323232}{333333}\)>\frac{333333333}{34343434}\)

\1+frac{-54}{55}=\frac{1}{55}\)

55^77 > 77^55