Question

S=3+3/2+3/2²+3/2³+....+3/2⁶

^{giúp mình nha}

Answer 1

\(S=3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+\frac{3}{2^4}+\frac{3}{2^5}+\frac{3}{2^6}\)

\(\Rightarrow2S=6+3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+\frac{3}{2^4}+\frac{3}{2^5}\)

\(\Rightarrow2S-S=\left(6+3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+\frac{3}{2^4}+\frac{3}{2^5}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+\frac{3}{2^4}+\frac{3}{2^5}+\frac{3}{2^6}\right)\)

\(\Rightarrow S=6-\frac{3}{2^6}\)

\(\Rightarrow S=6-\frac{3}{64}=5\frac{61}{64}=\frac{381}{64}\)

Answer 2

S=3+3/2+3/2²+3/2³+....+3/2⁶

=>2S=\(6+3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^5}\)

=>2S-S=\(6+3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^5}-3-\frac{3}{2}-\frac{3}{2^2}-\frac{3}{2^3}-...-\frac{3}{2^6}\)

=>S=\(6-\frac{3}{2^6}=6-\frac{3}{64}=\frac{381}{64}\)

Answer 3

nhân 2 vào thì thành \(2.\frac{3}{2^6}=\frac{3}{2^5}\)

Answer 4

cảm ơn bác à\

Answer 5

các bác cho em hoi vì sao ở S2 ta +6 mà bỏ 3/2⁶ ạ các bác giải thích nha