M = 2²⁰¹⁰-(2²⁰⁰⁹ + 2²⁰⁰⁸+....+2¹+2⁰

Đặt A =( 2²⁰⁰⁹+2²⁰⁰⁸+...2¹ +2⁰)

Suy ra 2A = 2²⁰¹⁰+2²⁰⁰⁹+2²⁰⁰⁸+...2²+2

Suy ra 2A-A = ( 2²⁰¹⁰+2²⁰⁰⁹+2²⁰⁰⁸+...+2²+2) - (2²⁰⁰⁹+ 2²⁰⁰⁸+...+2¹+2⁰)

Suy ra A= 2²⁰¹⁰-2⁰

Suy ra M = 2²⁰¹⁰-A=2^{2010 -} 2²⁰¹⁰+2⁰=1

Vậy M=1

Đúng nha

tui biet cach lam rui

hay qua

Câu 2:

\(a,\Rightarrow x=-23+15=-8\\ b,\Rightarrow5\left(x+4\right)=85\\ \Rightarrow x+4=17\Rightarrow x=13\\ c,\Rightarrow5^{x+2}=24+1=25=5^2\\ \Rightarrow x+2=2\Rightarrow x=0\\ d,\Rightarrow x+4+x+5⋮9\\ \Rightarrow2x+9⋮9\\ \Rightarrow2x⋮9\Rightarrow x\in\left\{0;9\right\}\left(0< x< 10\right)\)

mn người giúp mik với

a) ta có: A = 3^0 + 3^1 + 3^2 + ...+ 3^100

=> 3A = 3^1 + 3^2 + 3^3 + ...+ 3^101

=> 3A-A = 3^101 - 3^0

2A = 3^101 - 1

\(A=\frac{3^{101}-1}{2}\)

b) D = 1 - 5 + 5^2 - 5^3 + ...+ 5^98 - 5^99

=> 5D = 5 - 5^2 + 5^3 - 5^4+...+ 5^99 - 5^100

=> 5D+D = -5^100 + 1

6D = -5^100 + 1

\(D=\frac{-5^{100}+1}{6}\)

\(a,\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\left(\frac{3}{7}\right)^2\right)^{10}.\frac{3}{7}:\left(\frac{9}{49}\right)^6=\left(\frac{9}{49}\right)^{10}.\frac{3}{7}:\left(\frac{9}{49}\right)^6\)

\(=\left(\left(\frac{9}{49}\right)^{10}:\left(\frac{9}{49}\right)^6\right).\frac{3}{7}=\left(\frac{9}{49}\right)^{10-6}.\frac{3}{7}=\left(\frac{9}{49}\right)^4.\frac{3}{7}=\left(\left(\frac{3}{7}\right)^2\right)^4.\frac{3}{7}\)

\(=\left(\frac{3}{2}\right)^8.\frac{3}{7}=\left(\frac{3}{2}\right)^9\)

\(b,3-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2=3-1+\left(\frac{1}{2}\right)^2.\frac{1}{2}=2+\left(\frac{1}{2}\right)^3=2+\frac{1}{6}=2\frac{1}{6}\)

\(c,\left(0,125\right)^3.51=\left(\frac{1}{8}\right)^3.51=\frac{1^3}{8^3}.51=\frac{1}{512}.51=\frac{51}{512}\)

\(A=1+2^2+2^3+...+2^{2022}\)

\(\Rightarrow2A=2+2^3+2^4+...+2^{2023}\)

\(\Rightarrow A=2A-A=2+2^3+...+2^{2023}-1-2^2-...-2^{2022}=2-1+2^{2023}-2^2=-3+2^{2023}\)

A = 1 + 2² +  2³ + ..... + 2²⁰²¹ + 2²⁰²²

2A = 2(1 + 2² + 2³ + ..... + 2²⁰²¹ + 2²⁰²²)

2A = 2 + 2³ +  2⁴ + ..... + 2²⁰²² + 2²⁰²³

2A - A = (2+2³ + 2⁴ + ..... + 2²⁰²² + 2²⁰²³) - (1 + 2² + 2³ + .... + 2²⁰²¹ + 2²⁰²² )

Thấy sai sai sao í -))

2A=2²+2³+....+2²⁰²²)

2A-A=(2²+2³+...+2²⁰²²)-(2+2²+....+2²⁰²¹)

A=2²⁰²²-2

Đây nhé!