Roboguru

Diketahui  merupakan deret geometri dengan , , dan...

Diketahui begin mathsize 14px style a subscript 1 plus a subscript 2 plus. space. space. space plus a subscript n end style merupakan deret geometri dengan begin mathsize 14px style a subscript 1 equals x to the power of negative 2 end exponent end stylebegin mathsize 14px style a subscript 5 equals x squared end style, dan begin mathsize 14px style a subscript 6 equals 8 end style. Tentukan nilai dari:

begin mathsize 14px style a subscript 1 plus a subscript 2 plus a subscript 3 plus. space. space. space plus a subscript 7 end style 

  1. begin mathsize 14px style.... end style 

  2. undefined 

Jawaban:

Diketahui: begin mathsize 14px style a subscript 1 plus a subscript 2 plus. space. space. space plus a subscript n end style merupakan deret geometri dengan begin mathsize 14px style a subscript 1 equals x to the power of negative 2 end exponent end stylebegin mathsize 14px style a subscript 5 equals x squared end style, dan begin mathsize 14px style a subscript 6 equals 8 end style.

Ditanya: nilai dari: begin mathsize 14px style a subscript 1 plus a subscript 2 plus a subscript 3 plus. space. space. space plus a subscript 7 end style

Jawab: 

begin mathsize 14px style a subscript 1 equals x to the power of negative 2 end exponent a subscript 5 equals x squared a subscript 5 over a subscript 1 equals fraction numerator a r to the power of 4 over denominator a end fraction x squared over x to the power of negative 2 end exponent equals r to the power of 4 x to the power of 4 equals r to the power of 4 x equals r a subscript 6 equals a r to the power of 5 8 equals r to the power of negative 2 end exponent times r to the power of 5 8 equals r cubed r equals 2 x equals 2 a equals 2 to the power of negative 2 end exponent equals 1 fourth a subscript 1 plus a subscript 2 plus a subscript 3 plus a subscript 4 plus a subscript 5 plus a subscript 6 plus a subscript 7 equals S subscript 7 S subscript 7 equals fraction numerator a open parentheses r to the power of n minus 1 close parentheses over denominator r minus 1 end fraction equals fraction numerator begin display style 1 fourth end style open parentheses 2 to the power of 7 minus 1 close parentheses over denominator 2 minus 1 end fraction equals 1 fourth open parentheses 128 minus 1 close parentheses equals 127 over 4 end style 

 

0

Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved