[tex]( \frac{1 \times 2 \times 4 + 2 \times 4 \times 8 + ..... + n \times 2n \times 4n}{1 \times 3 \times 9 + 2 \times 6 \times 9 + ..... + n \times 3n \times 9n} ) {}^{ \frac{2}{3} } [/tex]
materi kelas 9
bantuin kak, besok rabu dikumpulkan
Nilai dari [tex](\sf \frac{1 \times 2 \times 4 + 2 \times 4 \times 8 + ..... + n \times 2n \times 4n}{1 \times 3 \times 9 + 2 \times 6 \times 9 + ..... + n \times 3n \times 9n} ) {}^{ \frac{2}{3} } [/tex] adalah [tex] \sf \boxed{ \sf \small \frac{4}{9} }[/tex]
Pembahasan:
[tex] \sf ( \dfrac{1 \times 2 \times 4 + 2 \times 4 \times 8 + ..... + n \times 2n \times 4n}{1 \times 3 \times 9 + 2 \times 6 \times 9 + ..... + n \times 3n \times 9n} ) {}^{ \frac{2}{3} }[/tex]
[tex] = \left( \sf \dfrac{n \times 2n \times 4n}{n \times 3n \times 9n} \right)^{ \frac{2}{3} } [/tex]
[tex] = \left( \sf \dfrac{ {8n}^{3} }{ {27n}^{3} } \right)^{ \frac{2}{3} } [/tex]
[tex] = \left( \sf \dfrac{ {8} }{ 27} \right)^{ \frac{2}{3} } [/tex]
[tex] = \left( \sf \dfrac{ {2}^{3} }{ {3}^{3} } \right)^{ \frac{2}{3} } [/tex]
[tex] \sf = \dfrac{ {2}^{2} }{ {3}^{2} } [/tex]
[tex] \sf = \boxed{ \sf \small \dfrac{4}{9} }[/tex]
[answer.2.content]
