Pertanyaan

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

Hitunglah jumlah setiap deret aritmetika berikut.

d. $\frac{1}{1 + 3} + (\frac{- 1}{2}) + \frac{1}{1 - 3} + ...$ sampai $10$ suku.

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

Jadi, jumlah 10 suku pertama adalah

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

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

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

Jadi, jumlah 10 suku pertama adalah

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