Câu hỏi của Kurenai Aki

Question

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 -.........

Phương Trâm · Accepted Answer

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 $72^{44}.71>72^{43}.71$

$\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}$Câu trả lời: 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 $72^{44}.71>72^{43}.71$

$\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}$

Phương Trâm · Answer

$A = 1 + 2 + 2^2 + 2^3+ ... + 2^{63}$

$2A=2+2^2+2^3+...+2^{63}+2^{64}$

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

$\Rightarrow A=2^{64}-1$Câu trả lời: $A = 1 + 2 + 2^2 + 2^3+ ... + 2^{63}$

$2A=2+2^2+2^3+...+2^{63}+2^{64}$

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

$\Rightarrow A=2^{64}-1$

Phương Trâm · Answer

$B = 5 + 5^2 + 5^3 + 5^4 +...+ 5^{100}$

$5B=5^2+5^3+5^4+...+5^{100}+5^{101}$

$5B-B=5^2+5^3+5^4+...+5^{100}+5^{101}-5-5^2-5^3-...-5^{99}-5^{100}$

$4B=5^2+5^3+5^4+...+5^{100}+5^{101}-\left(5+5^2+5^3+...+5^{99}+5^{100}\right)$

$4B=5^{101}-5$

$B=\frac{5^{101}-5}{4}$Câu trả lời: $B = 5 + 5^2 + 5^3 + 5^4 +...+ 5^{100}$

$5B=5^2+5^3+5^4+...+5^{100}+5^{101}$

$5B-B=5^2+5^3+5^4+...+5^{100}+5^{101}-5-5^2-5^3-...-5^{99}-5^{100}$

$4B=5^2+5^3+5^4+...+5^{100}+5^{101}-\left(5+5^2+5^3+...+5^{99}+5^{100}\right)$

$4B=5^{101}-5$

$B=\frac{5^{101}-5}{4}$

Đại số lớp 6