Question

cho c =1+4+4^2+...+4^100 va b =4^101 . chung minh rang c<b/3

 

Answer 1

<=> 4C = 4.( 1 + 4 + 4² + 4³ + .... + 4¹⁰⁰ )

<=> 4C = 4 + 4² + 4³ + 4⁴ + ..... + 4¹⁰¹

<=> 4C -C = ( 4 + 4² + 4³ + 4⁴ + ..... + 4¹⁰¹ ) - ( 1 + 4 + 4² + 4³ + .... + 4¹⁰⁰ )

<=> 3C = 4¹⁰¹ - 1

=> C = ( 4¹⁰¹ - 1 ) : 3

B : 3 = 4¹⁰¹ : 3

Vì ( 4¹⁰¹ - 1 ) : 3 < 4¹⁰¹ : 3 => C < B : 3

Vậy C < B : 3

Answer 2

4c=4+4^2+4^3+..+4^101

=>4c-c=(4+4^2+4^3+...+4^101)-(1+4+4^2+..+4^100)

=>3c=4^101-1

=>c=(4^101-1)/3

 Mà b=4^101=>b/3=4^101/3

 Ta thấy c=(4^101-1)/3<b/3=4^101/3

=>c<b/3(đpcm)

 Tick đi

Answer 3

kho qua