Roboguru
SD

Hitunglah jumlah setiap deret aritmetika berikut. d. 1+3​1​+(2−1​)+1−3​1​+... sampai 10 suku.

Pertanyaan

Hitunglah jumlah setiap deret aritmetika berikut.

d. begin mathsize 14px style fraction numerator 1 over denominator 1 plus square root of 3 end fraction plus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses plus fraction numerator 1 over denominator 1 minus square root of 3 end fraction plus... end style sampai begin mathsize 14px style 10 end style suku.

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style a equals fraction numerator 1 over denominator 1 plus square root of 3 end fraction end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row b equals cell fraction numerator negative 1 over denominator 2 end fraction minus fraction numerator 1 over denominator 1 plus square root of 3 end fraction end cell row blank equals cell fraction numerator negative left parenthesis 1 plus square root of 3 right parenthesis over denominator 2 open parentheses 1 plus square root of 3 close parentheses end fraction minus fraction numerator 1 over denominator 1 plus square root of 3 end fraction end cell row blank equals cell fraction numerator negative 2 minus square root of 3 minus 2 over denominator 2 plus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator negative 4 minus square root of 3 over denominator 2 plus 2 square root of 3 end fraction 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 n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis b right parenthesis end cell row cell S subscript 10 end cell equals cell 10 over 2 open parentheses 2 open parentheses fraction numerator 1 over denominator 1 plus square root of 3 end fraction close parentheses plus 10 open parentheses fraction numerator negative 4 minus square root of 3 over denominator 2 plus 2 square root of 3 end fraction close parentheses close parentheses end cell row blank blank blank row cell S subscript 10 end cell equals cell 5 open parentheses 2 open parentheses fraction numerator 1 over denominator 1 plus square root of 3 end fraction close parentheses plus 5 open parentheses fraction numerator negative 4 minus square root of 3 over denominator 1 plus square root of 3 end fraction close parentheses close parentheses end cell row cell S subscript 10 end cell equals cell fraction numerator 10 over denominator 1 plus square root of 3 end fraction plus fraction numerator negative 20 minus 5 square root of 3 over denominator 1 plus square root of 3 end fraction space end cell row cell S subscript 10 end cell equals cell fraction numerator negative 10 minus 5 square root of 3 over denominator 1 plus square root of 3 end fraction space end cell end table end style 

Jadi, jumlah 10 suku pertama adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 10 minus 5 square root of 3 over denominator 1 plus square root of 3 end fraction end cell end table end style

19

0.0 (0 rating)

Pertanyaan serupa

Tunjukkan bahwa dalam setiap deret aritmetika selalu berlaku: a. Sn+2​−2Sn+1​+Sn​=b

8

0.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia