Question

\(S=\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)

Answer 1

2S=\(\frac{6}{2}+\frac{6}{2^2}+....+\frac{6}{2^9}\)

2S-S=<\(\frac{6}{2}+\frac{6}{2^2}+....+\frac{6}{2^9}\).>-<\(\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)>

S=3+3+3+3+3+3+3+3+3

S=27

Answer 2

ta có : 

2.S=\(\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^{10}}\)

2.S-S=\(\left(\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^{10}}\right)-\left(\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)

S=\(\frac{3}{2^{10}}-\frac{3}{2}\)