Question

thu gọn các tổng

A=1+3+3²+3³+.........+3¹⁰⁰

Answer 1

Ta có: A = 1 + 3 + 3² + 3³ +.........+ 3¹⁰⁰

=> 3A =  3 + 3² + 3³ +.........+ 3¹⁰¹

=> 3A - A = 3¹⁰¹ - 1

=> 2A =  3¹⁰¹ - 1

=> A = 3¹⁰¹ - 1/2 

Answer 2

=>A.3=3+3²+3³+...3¹⁰⁰

2A=3¹⁰⁰-1

A=(3¹⁰⁰-1):2

Answer 3

A = 1 + 3 + 3 ²  + 3 ³   + ... + 3 ¹⁰⁰

3A  = 3 + 3 ²  + 3 ³ + 3 ⁴  +..... + 3 ¹⁰¹

3A - A = ( 3 + 3 ²  + 3 ³ + 3 ⁴  +..... + 3 ¹⁰¹ )

            - ( 1 + 3 + 3 ²  + 3 ³   + ... + 3 ¹⁰⁰  )

2A       = 3 ¹⁰¹ - 1

  A       = \(\frac{3^{101}-1}{2}\)