Jika diketahui bahwa \( x = 10-10 \frac{1}{3}+10 \frac{2}{3}-\cdots+40 \), nilai \(x\) yang memenuhi adalah…
- 1.150
- 1.125
- 690
- 45
- 25
(Soal SIMAK UI 2013)
Pembahasan:
Kita dapat manipulasi deret \( 10-10 \frac{1}{3}+10 \frac{2}{3}-\cdots+40 \) sehingga diperoleh bentuk:
\begin{aligned} & 10-10 \frac{1}{3}+10 \frac{2}{3}-\cdots+40 \\[8pt] &= \frac{1}{3} \left( 30-31+32-\cdots+120 \right) \\[8pt] &= \frac{1}{3} (30+32+34+ \cdots + 120) - \frac{1}{3}(31+33+35+ \cdots + 119) \\[8pt] &= \frac{1}{3} \left( \frac{46}{2} (30+120) \right)-\frac{1}{3} \left( \frac{45}{2} ( 31+119) \right) \\[8pt] &= \frac{1}{3} ( 46 \cdot 75) - \frac{1}{3} ( 45 \cdot 75) \\[8pt] &= \frac{1}{3} \cdot 75 (46-45) \\[8pt] &= \frac{1}{3} \cdot 75 = 25 \end{aligned}
Jawaban E.