| Diketahui |
Diketahui 3 pernyataan:
- \({S_{\left. {\overline {\, n \,}}\! \right| }} = {a_{\left. {\overline {\, n \,}}\! \right| }}{\left( {1 + i} \right)^n}\)
- \(\frac{1}{{{S_{\left. {\overline {\, n \,}}\! \right| }}}} + i = \frac{1}{{{a_{\left. {\overline {\, n \,}}\! \right| }}}}\)
- \(\frac{1}{{{a_{\left. {\overline {\, n \,}}\! \right| }}}} + i = \frac{1}{{{S_{\left. {\overline {\, n \,}}\! \right| }}}}\)
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| Proses pengerjaan |
Pernyataan I:
\({\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = {a_{\left. {\overline {\, n \,}}\! \right| }}{\left( {1 + i} \right)^n}\)
\(( \Leftarrow ){\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = \frac{{1 – {v^n}}}{i}{\left( {1 + i} \right)^n}\)
\(( \Leftarrow ){\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = \frac{{1 – {{(1 + i)}^{ – n}}}}{i}{\left( {1 + i} \right)^n}\)
\(( \Leftarrow ){\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = \frac{{1 – \frac{1}{{{{(1 + i)}^n}}}}}{i}{\left( {1 + i} \right)^n}\)
\(( \Leftarrow ){\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = \frac{{\frac{{{{(1 + i)}^n}}}{{{{(1 + i)}^n}}} – \frac{1}{{{{(1 + i)}^n}}}}}{i}{\left( {1 + i} \right)^n}\)
\(( \Leftarrow ){\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = \frac{{\frac{{{{(1 + i)}^n} – 1}}{{{{(1 + i)}^n}}}}}{i}{\left( {1 + i} \right)^n}\)
\(( \Leftarrow ){\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = \frac{{{{(1 + i)}^n} – 1}}{{i{{(1 + i)}^n}}}{\left( {1 + i} \right)^n}\)
\(( \Leftarrow ){\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = \frac{{{{(1 + i)}^n} – 1}}{i}\)
maka \({\rm{ }}{S_{\left. {\overline {\, n \,}}\! \right| }} = {a_{\left. {\overline {\, n \,}}\! \right| }}{\left( {1 + i} \right)^n}\)
Pernyataan II
\(\frac{1}{{{S_{\left. {\overline {\, n \,}}\! \right| }}}} + i = \frac{1}{{{a_{\left. {\overline {\, n \,}}\! \right| }}}}\)
\(( \Rightarrow ){\rm{ }}\frac{1}{{{S_{\left. {\overline {\, n \,}}\! \right| }}}} + i = \frac{i}{{{{(1 + i)}^n} – 1}} + i\)
\(( \Rightarrow ){\rm{ }}\frac{1}{{{S_{\left. {\overline {\, n \,}}\! \right| }}}} + i = \frac{{i + i{{(1 + i)}^n} – i}}{{{{(1 + i)}^n} – 1}}\)
\(( \Rightarrow ){\rm{ }}\frac{1}{{{S_{\left. {\overline {\, n \,}}\! \right| }}}} + i = \frac{i}{{1 – {v^n}}}\)
maka \(\frac{1}{{{S_{\left. {\overline {\, n \,}}\! \right| }}}} + i = \frac{1}{{{a_{\left. {\overline {\, n \,}}\! \right| }}}}\)
Pernyataan II benar maka pernyataan III tidak benar. |
