Question

1. Rút gọn tổng: 

a) A = 2^0 + 2^1 + 2^2 +...+ 2^50

b) B = 5 + 5^2 + 5^3 +...+ 5^99 + 5^100

c) C = 3 - 3^2 + 3^3 - 3^4 +...+ 3^2009 - 3 ^2010

2. Tìm x thuộc Z biết; 

( x + 2 ) + ( 4x + 4 ) + ( 7x + 6 ) +...+ ( 25x + 18 ) + ( 28x + 20 ) = 1560

Answer 1

Bài 1

a) A = 2^0 + 2^1 + 2^2 +...+ 2^50

2A=2^1+2^2+2^3+...+2^51

2A-A=(2^1+2^2+2^3+...+2^51)-(2^0 + 2^1 + 2^2 +...+ 2^50)

A=(2^1-2^1)+(2^2-2^2)+...+(2^50-2^50)+(2^51-2^1)

A=0+0+...+0+(2^51-2^1)

A=2^51-2^1

b)B = 5 + 5^2 + 5^3 +...+ 5^99 + 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=(5^2-5^2)+(5^3-5^3)+...+(5^100-5^100)+(5^101-5)

4B=0+0+...+0+(5^101-5)

4B=5^101-5

B=(5^101-5)/4

c)C = 3 - 3^2 + 3^3 - 3^4 +...+ 3^2009 - 3 ^2010

3C=3^2-3^3+3^4-3^5+...+3^2010-3^2011

3C-C=(3^2-3^3+3^4-3^5+...+3^2010-3^2011)-(3 - 3^2 + 3^3 - 3^4 +...+ 3^2009 - 3 ^2010)

...............................................!!!!!!!!!!!!!!!!!!!!!!!!

Bài 2

8(mình k0 chắc)

Answer 2

Làm bài 1 cũng đc rồi. Cảm ơn bạn nhiều

Answer 3

2)x=10