Question

Thu gọn tổng sau:

A = 1 + 3  + 3² + 3³ + ....+ 3¹⁰⁰

Answer 1

A = 1 + 3 + 3² + 3³ +....+ 3¹⁰⁰

3A = 3 + 3² + 3³ + 3⁴ +...+3¹⁰¹

=> 2A = 3A - A = 3¹⁰¹ - 1

=> A = \(\frac{3^{101}-1}{2}\)

Answer 2

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

=> 3A= 3+3²+3³+3⁴+...........+3¹⁰¹        (2)

Lấy (2)-(1) ta có:

3A-A=(3+3²+3³+3⁴+............+3¹⁰¹)-(1+3+3²+3³+.............+3¹⁰⁰)

=> 2A=3¹⁰¹-1

\(\Rightarrow A=\frac{3^{101}-1}{2}\)

Answer 3

A = 1 + 3  + 3² + 3³ + ....+ 3100

=> 3A=  3  + 3² + 3³ + ....+ 3¹⁰⁰

3A -A=( 3 +3² + 3³ +..... + 3¹⁰¹

2A =\(\frac{3^{101}-1}{2}\)

Answer 4

A=

3A=

A=

Answer 5

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

=> 3A = 3 + 3² + 3³ + 3⁴ +...+3¹⁰¹

=>  3A - A = 3¹⁰¹ - 1

=> 2A = 3¹⁰¹ - 1

=> A = 3¹⁰¹ - 1/2