A = 5 + 5² + 5³ + ... + 5⁴⁹ + 5⁵⁰

⇒ 5A = 5² + 5³ + 5⁴ + ... + 5⁵⁰ + 5⁵¹

⇒ 4A = 5A - A

= (5² + 5³ + 5⁴ + ... + 5⁵⁰ + 5⁵¹) - (5 + 5² + 5³ + ... + 5⁴⁹ + 5⁵⁰)

= 5⁵¹ - 5

⇒ A = (5⁵¹ - 5) : 4

\(A=2+2^2+...+2^{20}\)

\(2A=2^2+2^3+...+2^{21}\)

\(2A-A=2^2+2^3+...+2^{21}-2-2^2-...-2^{20}\)

\(A=2^{21}-2\)

___________

\(B=5+5^2+...+5^{50}\)

\(5B=5^2+5^3+...+5^{51}\)

\(5B-B=5^2+5^3+...+5^{51}-5-5^2-...-5^{50}\)

\(4B=5^{51}-5\)

\(B=\dfrac{5^{51}-5}{4}\)

___________

\(C=1+3+3^2+...+3^{100}\)

\(3C=3+3^2+...+3^{101}\)

\(3C-C=3+3^2+...+3^{101}-1-3-3^2-...-3^{100}\)

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

\(C=\dfrac{3^{101}-1}{2}\)

2A= 2(2+2²+2³+...+2¹⁹+2²⁰)

2A= 2²+2³+2⁴+...+2²⁰+2²¹

2A-A=(2²+2³+2⁴+...+2²⁰+2²¹)-(2+2²+2³+...+2¹⁹+2²⁰)

A=2²¹-2

Vậy A=2²¹-2

Làm tương tự nhee

khó v

Sửa câu a

a)Ta có:

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

 \(A=\left(3+3^2+3^3\right)+...+\left(3^{97}+3^{98}+3^{99}\right)\) 

\(A=\left(3+3^2+3^3\right)+...+3^{96}.\left(3+3^2+3^3\right)\)

\(A=39+...+3^{96}.39\)

\(A=39.\left(1+...+3^{96}\right)\)

Vì 39 \(⋮\) 13 nên 39 . ( 1 + ... + 3⁹⁶ ) \(⋮\) 13

Vậy A \(⋮\) 13

_________

b)Ta có:

 \(B=5+5^2+5^3+...+5^{50}\)

\(B=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{49}+5^{50}\right)\)

\(B=\left(5+5^2\right)+5^2.\left(5+5^2\right)+...+5^{48}.\left(5+5^2\right)\)

\(B=30+5^2.30+...+5^{48}.30\)

\(B=30.\left(1+5^2+...+5^{48}\right)\)

Vì 30 \(⋮\) 6 nên 30. ( 1 + 5² + ... + 5⁴⁸ ) \(⋮\) 6

Vậy B \(⋮\) 6

a,A=3+3²+3³+..+3⁹⁹=(3+3²+3³)+...+(3⁹⁷+3⁹⁸+3⁹⁹)

     =3(1+3+3²)+...+3⁹⁷(1+3+3²)=3x13+...+3⁹⁷x13=13(3+...+97)⋮13

b,B=5+5²+...+5⁵⁰=(5+5²)+...+(5⁴⁹+5⁵⁰)=5(1+5)+..+5⁴⁹(1+5)

  =5x6+...+5⁴⁹x6=6(5+..+5⁴⁹)⋮6.

Ta có A = 5 + 5² + 5³ + ... + 5²⁰²¹

5A = 5² + 5³ + 5⁴ + ... + 5²⁰²²

5A - A = ( 5² + 5³ + 5⁴ + ... + 5²⁰²² ) - ( 5 + 5² + 5³ + ... + 5²⁰²¹ )

4A = 5²⁰²² - 5

A = \(\dfrac{5^{2022}-5}{4}\)

Tìm chữ số tận cùng của kết quả mỗi phép tính sau:

a. 49¹⁵

b. 54¹⁰

c. 11²⁰+119²¹+2000²²

Bài 1:
a.

\(\frac{1}{2\sqrt{2}-3\sqrt{3}}=\frac{2\sqrt{2}+3\sqrt{3}}{(2\sqrt{2}-3\sqrt{3})(2\sqrt{2}+3\sqrt{3})}=\frac{2\sqrt{2}+3\sqrt{3}}{(2\sqrt{2})^2-(3\sqrt{3})^2}=\frac{2\sqrt{2}+3\sqrt{3}}{-19}\)

b.

\(=\sqrt{\frac{(3-\sqrt{5})^2}{(3-\sqrt{5})(3+\sqrt{5})}}=\sqrt{\frac{(3-\sqrt{5})^2}{3^2-5}}=\sqrt{\frac{(3-\sqrt{5})^2}{4}}=\sqrt{(\frac{3-\sqrt{5}}{2})^2}=|\frac{3-\sqrt{5}}{2}|=\frac{3-\sqrt{5}}{2}\)

Bài 2.

a. 

\(=\frac{\sqrt{8}(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}=\frac{2\sqrt{2}(\sqrt{5}+\sqrt{3})}{5-3}=\sqrt{2}(\sqrt{5}+\sqrt{3})=\sqrt{10}+\sqrt{6}\)

b.

\(=\sqrt{\frac{(2-\sqrt{3})^2}{(2-\sqrt{3})(2+\sqrt{3})}}=\sqrt{\frac{(2-\sqrt{3})^2}{2^2-3}}=\sqrt{(2-\sqrt{3})^2}=|2-\sqrt{3}|=2-\sqrt{3}\)

Bài 3:

a.

\(M=\left[\frac{15(\sqrt{6}-1)}{(\sqrt{6}+1)(\sqrt{6}-1)}+\frac{4(\sqrt{6}+2)}{(\sqrt{6}-2)(\sqrt{6}+2)}-\frac{12(3+\sqrt{6})}{(3-\sqrt{6})(3+\sqrt{6})}\right](\sqrt{6}+11)\)

\(=\left[\frac{15(\sqrt{6}-1)}{6-1}+\frac{4(\sqrt{6}+2)}{6-2^2}-\frac{12(3+\sqrt{6})}{3^2-6}\right](\sqrt{6}+11)\)

\(=[3(\sqrt{6}-1)+2(\sqrt{6}+2)-4(3+\sqrt{6})](\sqrt{6}+11)=(\sqrt{6}-11)(\sqrt{6}+11)=6-11^2=-115\)

b.

\(N=\left[1-\frac{\sqrt{5}(\sqrt{5}+1)}{\sqrt{5}+1}\right].\left[\frac{\sqrt{5}(\sqrt{5}-1)}{1-\sqrt{5}}-1\right]\)

\(=(1-\sqrt{5})(-\sqrt{5}-1)=(\sqrt{5}-1)(\sqrt{5}+1)=5-1=4\)

\(=a^2+2a+1-a^2+2a-1-3a^2+3\\ =-3a^2+4a+3\)

TH1: x>=5/3

A=3x-5+4x-6=7x-11

TH2: 3/5<x<5/3

A=5-3x+4x-6=x-1

Sao ko bảo chị giải đi, kkkk

Haizzzzz

Câu a)

Câu b) Đề bài sai.