S = 1 + 3 + 3² + 3³ + ... + $3^{20}$
3 . S = 3 . (1 + 3 + 3² + 3³ + ... + $3^{20}$)
3 . S = 3 + 3² + 3³ + $3^{4}$ + ... + $3^{21}$
3 . S - S = (3 + 3² + 3³ + $3^{4}$ + ... + $3^{21}$) - (1 + 3 + 3² + 3³ + ... + $3^{20}$)
2 . S = $3^{21}$ - 1
S = ($3^{21}$ - 1) : 2 = $\frac{3^{21} - 1}{2}$
b) 2 . S + 1 = $3^{n}$
⇔ $3^{21}$ - 1 + 1 = $3^{n}$
⇔ $3^{21}$ = $3^{n}$
⇔ n = 21
Chúc học tốt!!!