Question

[Cún Dễ Thương]

Rút gọn:

a, C=1+3+3^2+3^3+.....................................+3^20

b, B=2+2^2+2^3+.........................................+2^49+2^50

Answer 1

[Đinh Đức Hùng]

a ) C = 1 + 3 + 3² + 3³ + ....... + 3²⁰

<=> 3C = 3.( 1 + 3 + 3² + 3³ + ...... + 3²⁰ )

<=> 3C = 3 + 3² + 3³ + 3⁴ + ....... + 3²¹

<=> 3C - C = ( 3 + 3² + 3³ + 3⁴ + ....... + 3²¹ ) - ( 1 + 3 + 3² + 3³ + ...... + 3²⁰ )

<=> 2C = 3²¹ - 1

=> C = ( 3²¹ - 1 ) : 2

b ) B = 2 + 2² + 2³ + ...... + 2⁵⁰

<=> 2B = 2.( 2 + 2² + 2³ + ...... + 2⁵⁰ )

<=> 2B = 2² + 2³ + 2⁴ + ....... + 2⁵¹

<=> 2B - B = ( 2² + 2³ + 2⁴ + ...... + 2⁵¹ ) - ( 2 + 2² + 2³ + ...... + 2⁵⁰ )

=> B = 2⁵¹ - 2

Answer 2

[Kiều Bích Huyền]

a, Ta có: 3C=3+3^2+3^3+3^4+...+3^21

  3C-C=(3+3^2+3^3+...+3^20+3^21)-(1+3+3^2+...+3^19+3^20)

<=>2C = 3^21 - 1 - 3^20 =3^20. (3-1) -1=3^20 .2 -1

=>C\(=\frac{3^{20}.2-1}{2}=3^{20}-\frac{1}{2}=3^{20}-0,5\)