Question

thu gọn:

A=1+2 mũ1+2 mũ2+2 mũ3+...+2 mũ9+2 mũ10

B=1+3 mũ 1+3 mũ 2+3 mũ 3+...+3 mũ 9+3 mũ 10

Answer 1

A = 1+2+2²+...+2¹⁰

=> 2A = 2+2²+2³+...+2¹¹

=> 2A - A = (2+2²+2³+...+2¹¹) - (1+2+2²+...+2¹⁰)

=> A = 2¹¹ - 1

B = 1+3+3²+...+3¹⁰

=> 3B = 3+3²+3³+...+3¹¹

=> 3B - B = (3+3²+3³+...+3¹¹) - (1+3+3²+...+3¹⁰)

=> 2B = 3¹¹ - 1

=> B = \(\frac{3^{11}-1}{2}\)

Answer 2

A = 1 + 2 ¹ + 2 ² + 2 ³ + ... + 2 ⁹ + 2 ¹⁰

2A = 2 + 2 ² + 2 ³ + 2 ⁴ + ... + 2 ¹⁰  + 2 ¹¹

2A - A = ( 2 + 2 ² + 2 ³ + 2 ⁴ + ... + 2 ¹⁰  + 2 ¹¹ ) 

           - ( 1 + 2 ¹ + 2 ² + 2 ³ + ... + 2 ⁹ + 2 ¹⁰  )

   A     = 2 ¹¹  - 1

   A     = 2047

B = 1 + 3 ¹ + 3 ² + 3 ³ + ... + 3 ⁹  + 3 ¹⁰

3B = 3 ¹ + 3 ² + 3 ³ + 3 ⁴ + ... + 3 ¹⁰  + 3 ¹¹

3B - B= ( 3 ¹ + 3 ² + 3 ³ + 3 ⁴ + ... + 3 ¹⁰  + 3 ¹¹ )

            - ( 1 + 3 ¹ + 3 ² + 3 ³ + ... + 3 ⁹  + 3 ¹⁰ )

 2B    = 3 ¹¹ - 1

B       = \(\frac{3^{11}-1}{2}\)

B = 88573