Question

1+3+3²+...+3¹¹⁹

Answer 1

Đặt S=1+3+3²+...+3¹¹⁹

3S=3+3²+3³+...+3¹²⁰

3S-S=(3+3²+3³+...+3¹²⁰)-(1+3+3²+...+3¹¹⁹)

2S=3¹²⁰-1

=>S=\(\frac{3^{120}-1}{2}\)

Answer 2

S= \(1+3^2+...+3^{119}\)

=> 3S=\(3+3^2+...+3^{120}\)

=> 2S =\(3^{120}-1\)

\(S=\frac{3^{120}-1}{2}\)

Answer 3

Đặt S = 1+3+3²+.....+ 3¹⁹⁹

3S= 3+3²+3³+.....+3²⁰⁰

3S-S= (3+3²+3³+.....+3²⁰⁰) - (1+3+3²+....... +3¹⁹⁹)
2S=3²⁰⁰- 1

S= \(\frac{3^{200}-1}{2}\)