Toán Giải hộ mik : S=1+1/3+1/9+1/27+…1/2187 12/09/2021 By Rose Giải hộ mik : S=1+1/3+1/9+1/27+…1/2187
Đáp án: $S = \frac{{3280}}{{2187}}$ Giải thích các bước giải: $\begin{array}{l} S = 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + … + \frac{1}{{2187}}\\ \Rightarrow 3 \times S = 3 \times 1 + 3 \times \frac{1}{3} + 3 \times \frac{1}{9} + 3 \times \frac{1}{{27}} + … + 3 \times \frac{1}{{2187}}\\ \Rightarrow 3S = 3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + … + \frac{1}{{729}}\\ \Rightarrow 3S – S = \left( {3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + … + \frac{1}{{729}}} \right) – \left( {1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + … + \frac{1}{{2187}}} \right)\\ \Rightarrow 2S = 3 – \frac{1}{{2187}} = \frac{{3 \times 2187 – 1}}{{2187}} = \frac{{6560}}{{2187}}\\ \Rightarrow S = \frac{{3280}}{{2187}}\\ \end{array}$ Trả lời
Đáp án:
$S = \frac{{3280}}{{2187}}$
Giải thích các bước giải:
$\begin{array}{l}
S = 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + … + \frac{1}{{2187}}\\
\Rightarrow 3 \times S = 3 \times 1 + 3 \times \frac{1}{3} + 3 \times \frac{1}{9} + 3 \times \frac{1}{{27}} + … + 3 \times \frac{1}{{2187}}\\
\Rightarrow 3S = 3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + … + \frac{1}{{729}}\\
\Rightarrow 3S – S = \left( {3 + 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + … + \frac{1}{{729}}} \right) – \left( {1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + … + \frac{1}{{2187}}} \right)\\
\Rightarrow 2S = 3 – \frac{1}{{2187}} = \frac{{3 \times 2187 – 1}}{{2187}} = \frac{{6560}}{{2187}}\\
\Rightarrow S = \frac{{3280}}{{2187}}\\
\end{array}$