a.                            54

b.                             52  

A)\(M=1+3+3^2+...+3^9\)\(\Rightarrow3M=3+3^2+3^3+...+3^{10}\)\(\Rightarrow3M-M=\left(3+3^2+3^3+...+3^{10}\right)-\left(1+3+3^2+...+3^9\right)\)

\(\Rightarrow2M=3^{10}-1\)\(\Rightarrow2M+1=3^{10}\)\(\Rightarrow n=10\)

B) \(A=1+4^2+...+4^{99}\)\(\Rightarrow4A=4+4^3+4^4+...+4^{100}\)\(\Rightarrow4A-A=\left(4+4^3+4^4+...+4^{100}\right)-\left(1+4^2+...+4^{99}\right)\)

\(\Rightarrow3A=4^{100}+4-4^2-1\Rightarrow3A=4^{100}-13\Rightarrow3A+13=4^{100}\Rightarrow n=100\)

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

câu sau sai đề phải

\(A=3+3^2+3^3+....+3^{99}\)

\(3A=3^2+3^3+...+3^{99}\)

\(3A-A=\left(3^2+3^3+...+3^{100}\right)-\left(3+3^2+3^3+....+3^{99}\right)\)

\(\Rightarrow A=\frac{3^{100}-1}{3}\)

Câu a mk ko hiểu gì nha xl bn nhìu

b)1-2+3-4+...+99-100

=(1-2)+(3-4)+...+(99-100)

=(-1)+(-1)+...+(-1)

=(-1) . 50

=(-50)

c) 5 + 5² + 5³ + ...+ 5⁹⁹ + 5¹⁰⁰ 

=(5+5²)+(5³+5⁴)+....+(5⁹⁹+5¹⁰⁰)

=30+5²(5+5²)+...+5⁹⁸(5+5²)

=30.1+5².30+.....+5⁹⁸.30

=30(1+5²+...+5⁹⁸) chia hết cho 6

3A = 3² + 3³ + 3⁴ + ... + 3¹⁰⁰ + 3¹⁰¹

=> 3A - A = 2A = (3² + 3³ + 3⁴ + ... + 3¹⁰⁰ + 3¹⁰¹) - (3 + 3² + 3³ +..... + 3⁹⁹ + 3¹⁰⁰)

=> 2A = 3¹⁰¹ - 3

=> 2A + 3 = 3¹⁰¹ => N = 101