Latihan Khusus UN IPA 2016/2017 [HKM] [MATEMATIKA] Jika 3p = (4⁻¹ - 1)(1 - 5⁻ ¹)(6⁻¹ - 1)(1 - 7⁻¹)(8⁻¹ - 1)(1 - 9⁻¹)(10⁻¹ - 1) maka nilai 10p = ... (A) - 10 (B)

≡ Penyelesaian:
⇒ [tex]3p=(4^{-1}-1)(1-5^{-1})(6^{-1}-1)(1-7^{-1})(8^{-1}-1)(1-9^{-1})(10^{-1}-1)[/tex]
⇒ [tex]3p=(\frac{1}{4}-1)(1-\frac{1}{5})(\frac{1}{6}-1)(1-\frac{1}{7})(\frac{1}{8}-1)(1-\frac{1}{9})(\frac{1}{10}-1)[/tex]
⇒ [tex]3p=(-\frac{3}{4}).(\frac{4}{5}).(-\frac{5}{6}).(\frac{6}{7}).(-\frac{7}{8}).(\frac{8}{9}).(-\frac{9}{10})[/tex]

⇒ [tex]10p=(3p).( \frac{10}{3}) [/tex]
⇒ [tex]10p=(-\frac{3}{4}).(\frac{4}{5}).(-\frac{5}{6}).(\frac{6}{7}).(-\frac{7}{8}).(\frac{8}{9}).(-\frac{9}{10}).(\frac{10}{3})[/tex]
∴ [tex]\boxed{10p=1}[/tex]