Tentukan nilai n jika diketahui pernyataan berikut ini. c. P(n,5)=9P(n−1,4)

Pertanyaan

Tentukan nilai $\style{font-size:14px}n$ jika diketahui pernyataan berikut ini.

c. $\style{font-size:14px}{P(n,5)=9P(n-1,4)}$

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

berdasarkan pernyataan

diperoleh

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses n comma 5 close parentheses end cell equals cell 9 P left parenthesis n minus 1 , 4 right parenthesis end cell row cell fraction numerator n factorial over denominator open parentheses n minus 5 close parentheses factorial end fraction end cell equals cell 9 times fraction numerator open parentheses n minus 1 close parentheses factorial over denominator open parentheses open parentheses n minus 1 close parentheses minus 4 close parentheses factorial end fraction end cell row cell fraction numerator n times left parenthesis n minus 1 right parenthesis times left parenthesis n minus 2 right parenthesis times left parenthesis n minus 3 right parenthesis times left parenthesis n minus 4 right parenthesis times left parenthesis n minus 5 right parenthesis factorial over denominator open parentheses n minus 5 close parentheses factorial end fraction end cell equals cell 9 times fraction numerator open parentheses n minus 1 close parentheses times left parenthesis n minus 2 right parenthesis times left parenthesis n minus 3 right parenthesis times left parenthesis n minus 4 right parenthesis times left parenthesis n minus 5 right parenthesis factorial over denominator open parentheses n minus 5 close parentheses factorial end fraction end cell row cell n times open parentheses n minus 1 close parentheses times open parentheses n minus 2 close parentheses times open parentheses n minus 3 close parentheses times open parentheses n minus 4 close parentheses end cell equals cell 9 times open parentheses n minus 1 close parentheses times left parenthesis n minus 2 right parenthesis times left parenthesis n minus 3 right parenthesis times left parenthesis n minus 4 right parenthesis end cell row n equals 9 end table end style$

Jadi, berdasarkan pernyataan diperoleh .