Pertanyaan

Diketahui deret geometri: 256 + 128 + 64 + ... + U n = 511 Tentukan nilai n!

Diketahui deret geometri:

$256 + 128 + 64 + ... + U_{n} = 511$

Tentukan nilai n!

S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai n adalah 9

Pembahasan

Diketahui: Jadi, nilai n adalah 9

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight r equals cell straight U subscript 2 over straight U subscript 1 end cell row blank equals cell 128 over 256 end cell row straight r equals cell 1 half end cell end table end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell fraction numerator a open parentheses 1 minus r to the power of n close parentheses over denominator 1 minus r end fraction end cell row 511 equals cell fraction numerator 256 open parentheses 1 minus open parentheses begin display style 1 half end style close parentheses to the power of n close parentheses over denominator 1 minus begin display style 1 half end style end fraction end cell row 511 equals cell fraction numerator 256 open parentheses 1 minus open parentheses begin display style 1 half end style close parentheses to the power of n close parentheses over denominator begin display style 1 half end style end fraction end cell row 511 equals cell 2 cross times 256 cross times open parentheses 1 minus open parentheses 1 half close parentheses to the power of n close parentheses end cell row 511 equals cell 512 cross times open parentheses 1 minus open parentheses 1 half close parentheses to the power of n close parentheses end cell row cell 511 over 512 end cell equals cell 1 minus open parentheses 1 half to the power of n close parentheses end cell row cell open parentheses 1 half close parentheses to the power of n end cell equals cell 1 minus 511 over 512 end cell row cell open parentheses 1 half close parentheses to the power of n end cell equals cell 1 over 512 end cell row cell open parentheses 1 half close parentheses to the power of n end cell equals cell open parentheses 1 half close parentheses to the power of 9 end cell row n equals 9 end table end style$

Jadi, nilai n adalah 9