Roboguru

Hitunglah: e.   sampai suku ke-n.

Pertanyaan

Hitunglah:

e. open parentheses a minus b close parentheses squared plus open parentheses a squared plus b squared close parentheses plus left parenthesis a plus b right parenthesis squared plus horizontal ellipsis  sampai suku ke-n.

Pembahasan Soal:

Diketahui deret aritmetika: open parentheses a minus b close parentheses squared plus open parentheses a squared plus b squared close parentheses plus left parenthesis a plus b right parenthesis squared plus horizontal ellipsis   

straight a equals left parenthesis a minus b right parenthesis squared equals a to the power of 2 end exponent plus b squared minus 2 a b straight b equals left parenthesis a squared plus b squared right parenthesis minus left parenthesis a minus b right parenthesis squared equals a to the power of 2 end exponent plus b squared minus open parentheses a squared plus b squared minus 2 a b close parentheses equals 2 a b     

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell straight S subscript straight n end cell equals cell straight n over 2 open parentheses 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight b close parentheses end cell row blank equals cell n over 2 open parentheses 2 open parentheses a squared plus b squared minus 2 a b close parentheses plus left parenthesis n minus 1 right parenthesis open parentheses 2 a b close parentheses close parentheses end cell row blank equals cell n over 2 open parentheses 2 a squared plus 2 b squared minus 4 a b plus 2 a b n minus 2 a b close parentheses end cell row blank equals cell n over 2 open parentheses 2 a squared plus 2 b squared minus 6 a b plus 2 a b n close parentheses end cell row blank equals cell a squared n plus b squared n minus 3 a b n plus a b n squared end cell end table     

Jadi, jumlah n suku pertama deret tersebut adalah Error converting from MathML to accessible text..

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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