Question

[Nghĩa Nguyễn Trọng]

Tính S = 3^10 + 3^11 + 3^12 +...+3^31. Giúp  Mình Mình Câu Like cho <3 Nhìu. Chúc Các bn nghỉ hè vui vẻ

Answer 1

[Thắng Nguyễn]

3S=3(3¹⁰+3¹¹+...+3³¹)

3S=3¹¹+3¹²+...+3³²

3S-S=(3¹¹+3¹²+...+3³²)-(3¹⁰+3¹¹+...+3³¹)

2S=3³²-3¹⁰

S=(3³²-3¹⁰):2

Answer 2

[Trần Tiến Minh]

\(S=3^{10}+3^{11}+3^{12}+...+3^{31}\)

\(\Leftrightarrow3S=3^{11}+3^{12}+3^{13}+...+3^{32}\)

\(\Rightarrow3S-S=\left(3^{11}+3^{12}+3^{13}+...+3^{32}\right)-\left(3^{10}+3^{11}+3^{12}+...+3^{31}\right)\)\(\Rightarrow2S=3^{32}-3^{10}\Rightarrow S=\frac{3^{32}-3^{10}}{2}\)