Question

[An Bùi]

thu gọn tổng sau 

B=1+3+3²+3³+...+3¹⁰⁰+3¹⁰¹

Answer 1

[Hồng Phúc]

\(B=1+3+3^2+3^3+...+3^{100}+3^{101}\)

\(\Rightarrow3B=3+3^2+3^3+3^4+...+3^{101}+3^{102}\)

\(\Rightarrow3B-B=3^{102}-1\)

\(\Leftrightarrow2B=3^{102}-1\)

\(\Leftrightarrow B=\dfrac{3^{102}-1}{2}\)