Pertanyaan

Tunjukkan bahwa dalam setiap deret aritmetika selalu berlaku: c. S 3 n = 3 ( S 2 n − S n )

Tunjukkan bahwa dalam setiap deret aritmetika selalu berlaku:

c. $S_{3 n} = 3 (S_{2 n} - S_{n})$

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 left parenthesis S subscript 2 n end subscript minus S subscript n right parenthesis end cell equals cell 3 open parentheses fraction numerator 2 n over denominator 2 end fraction open parentheses a plus U subscript 2 n end subscript close parentheses minus n over 2 left parenthesis a plus U subscript n right parenthesis close parentheses end cell row blank equals cell 3 open parentheses n over 2 open parentheses 2 a plus 2 U subscript 2 n end subscript minus a minus U subscript n close parentheses close parentheses end cell row blank equals cell 3 open parentheses n over 2 left parenthesis 2 a plus 2 U subscript 2 n end subscript minus a minus U subscript n right parenthesis close parentheses end cell row blank equals cell 3 open parentheses n over 2 open parentheses a plus 2 U subscript 2 n end subscript minus U subscript n close parentheses close parentheses end cell row blank equals cell 3 open parentheses n over 2 left parenthesis a plus 2 U subscript 2 n end subscript minus U subscript n right parenthesis close parentheses end cell row blank equals cell 3 open parentheses n over 2 left parenthesis a plus U subscript 3 right parenthesis close parentheses end cell row blank equals cell fraction numerator 3 n over denominator 2 end fraction left parenthesis a plus U subscript 3 right parenthesis end cell row blank equals cell S subscript 3 n end subscript end cell end table end style$