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Jika beda pada barisan aritmetika adalah dua kali suku pertama, buktikan bahwa: S m ​ S n ​ ​ = m 2 n 2 ​ .

Jika beda pada barisan aritmetika adalah dua kali suku pertama, buktikan bahwa: 

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M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

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Pembahasan

Maka,

begin mathsize 14px style b equals 2 a 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 open parentheses n minus 1 close parentheses b right parenthesis end cell row cell S subscript n end cell equals cell n over 2 left parenthesis 2 a plus open parentheses n minus 1 close parentheses 2 a right parenthesis end cell row cell S subscript n end cell equals cell n over 2 left parenthesis 2 a plus 2 a n minus 2 a right parenthesis end cell row cell S subscript n end cell equals cell n over 2 left parenthesis 2 a n right parenthesis end cell row cell S subscript n end cell equals cell a n squared end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S blank subscript n end cell equals cell n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis b right parenthesis space end cell row cell S blank subscript n end cell equals cell n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis 2 a right parenthesis space end cell row cell S blank subscript m end cell equals cell m over 2 left parenthesis 2 a plus 2 a m minus 2 a right parenthesis space end cell row cell S blank subscript m end cell equals cell m over 2 left parenthesis 2 a m right parenthesis space end cell row cell S blank subscript m end cell equals cell a m blank squared end cell end table end style

Maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator S n over denominator S blank subscript m end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator a n blank squared over denominator a m squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator S n over denominator S blank subscript m end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell n squared over m squared end cell end table end style

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Yolanda Sitanggang

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