Question

Rút gọn \(T=1+3^3+3^6+...+3^{105}\)

Answer 1

T = 1 + 3³ + 3⁶ + .... + 3¹⁰⁵

3³T = 3³  + 3⁶ + 3⁹ + .... + 3¹⁰⁸

27T - T = (3³ + 3⁶ + 3⁹ + .... + 3¹⁰⁸) - (1 + 3³ + 3⁶ + .... + 3¹⁰⁵)

26T = 3¹⁰⁸ - 1

T = (3¹⁰⁸ - 1) : 26

Ủng hộ mk nha !!! ^_^

Answer 2

Theo đàu bài ta có:
\(T=1+3^3+3^6+...+3^{105}\)
\(\Rightarrow T\cdot3^3=3^3+3^6+3^9+...+3^{108}\)
\(\Rightarrow T\cdot27-T=\left(3^3+3^6+3^9+...+3^{108}\right)-\left(1+3^3+3^6+...+3^{105}\right)\)
\(\Rightarrow T\cdot26=3^{108}-1\)
\(\Rightarrow T=\frac{3^{108}-1}{26}\)

Answer 3

\(T=\frac{3^{108}-1}{26}\)