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Dalam deret aritmetika apabila Sm​Sn​​=m2n2​, buktikan bahwa: Um​Un​​=2m−12n−1​.

Pertanyaan

Dalam deret aritmetika apabila begin mathsize 14px style S subscript n over S subscript m equals n squared over m squared end style, buktikan bahwa: begin mathsize 14px style U subscript n over U subscript m equals fraction numerator 2 n minus 1 over denominator 2 m minus 1 end fraction end style

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style S subscript n equals n over 2 open parentheses a plus U subscript n close parentheses n squared equals n over 2 open parentheses a plus U subscript n close parentheses a plus U subscript n equals fraction numerator n squared over denominator begin display style n over 2 end style end fraction a plus U subscript n equals 2 n U subscript n equals 2 n minus 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 a plus U subscript n right parenthesis space end cell row cell S subscript m end cell equals cell n over 2 left parenthesis a plus U subscript m right parenthesis end cell row cell m squared end cell equals cell m over 2 left parenthesis a plus U subscript m right parenthesis end cell row cell a plus U subscript m end cell equals cell fraction numerator m squared over denominator begin display style m over 2 end style end fraction end cell row cell a plus U subscript m end cell equals cell 2 m end cell row cell U subscript m end cell equals cell 2 n minus a end cell end table end style

Maka,

begin mathsize 14px style U subscript n over U subscript m equals fraction numerator 2 n minus a over denominator 2 m minus a end fraction end style 

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Sn​ adalah jumlah n suku pertama deret aritmetika. Jika a adalah suku pertama dan b beda deret itu, maka nilai Sn+2​−Sn​ adalah ....

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