Question

S = 1+3+3^2+3^3+3^4+ ....+3^20

SO SANH S VOI 1/2 . 3 ^ 31

Answer 1

Ta có: \(S=1+3+3^2+...+3^{20}\)

\(\Rightarrow3S=3+3^2+3^3+...+3^{21}\)

\(\Rightarrow3S-S=\left(3+3^2+3^3+...+3^{21}\right)-\left(1+3+3^2+...+3^{20}\right)\)

\(\Rightarrow2S=3^{21}-1\)

\(\Rightarrow S=\left(3^{21}-1\right).\frac{1}{2}\)

\(\Rightarrow S=3^{21}.\frac{1}{2}-\frac{1}{2}\)

Vì \(3^{21}.\frac{1}{2}-\frac{1}{2}< 3^{21}.\frac{1}{2}\) nên \(A< \frac{1}{2}.3^{21}\)

Vậy \(A< \frac{1}{2}.3^{21}\)