Question

[Kurenai Aki]

So sánh

a/72⁴⁵ - 72⁴⁴ và 72⁴⁴ - 72⁴³

b/1990¹⁶ + 1990⁹ và 1991¹⁰

Tính tổng

A = 1 + 2 + 2² + 2³+ ........... + 2⁶³

B = 5 + 5² + 5³ + 5⁴ +.....................+ 5¹⁰⁰

C = - 1² + 2² - 3² + 4² -..........- 19² + 20²

D = 9 + 99 + 999 +...............+ 9999....999

50 chữ số 9

Answer 1

[Phương Trâm]

a. Ta có:

\(72^{45}-72^{44}=72^{44}.\left(72-1\right)=72^{44}.71\)

\(72^{44}-72^{43}=72^{43}.\left(72-1\right)=72^{43}.71\)

Vì \(72^{44}.71>72^{43}.71\)

\(\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)

Answer 2

[Phương Trâm]

\(A = 1 + 2 + 2^2 + 2^3+ ... + 2^{63}\)

\(2A=2+2^2+2^3+...+2^{63}+2^{64}\)

\(2A-A=2+2^2+2^3+...+2^{63}+2^{64}-\left(1+2+2^2+2^3+...+2^{63}\right)\)

\(\Rightarrow A=2^{64}-1\)