Pertanyaan

x → ∞ lim 2 1 x 2 + 1 1 + 2 + 3 + ... + x ialah

$x \to \infty lim \frac{1 + 2 + 3 + ... + x}{\frac{1}{2} x ^{2} + 1} ialah$

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Bentuk dapat disederhanakan dengan rumus Sn pada barisan aritmatika yaitu Substitusikan ke soal. Jadi nilai dari adalah

Bentuk dapat disederhanakan dengan rumus Sn pada barisan aritmatika yaitu

begin mathsize 14px style S subscript n equals n over 2 open parentheses a plus U subscript n close parentheses S subscript x equals x over 2 left parenthesis 1 plus x right parenthesis end style

Substitusikan S subscript x ke soal.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 1 plus 2 plus 3 plus... plus x over denominator begin display style 1 half x squared plus 1 end style end fraction space end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style x over 2 end style open parentheses 1 plus x close parentheses over denominator begin display style 1 half end style x squared plus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 1 half x squared plus begin display style 1 half x end style over denominator 1 half x squared plus 1 end fraction end cell row blank blank cell Bagikan space denga n space pangkat space tertinggi space yaitu space straight x squared end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 1 half plus begin display style fraction numerator 1 over denominator 2 x end fraction end style over denominator 1 half plus begin display style 1 over x squared end style end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow infinity of 1 half plus begin display style limit as x rightwards arrow infinity of fraction numerator 1 over denominator 2 x end fraction end style over denominator limit as x rightwards arrow infinity of 1 half plus limit as x rightwards arrow infinity of begin display style 1 over x squared end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half plus 0 end style over denominator begin display style 1 half plus 0 end style end fraction end cell row blank equals 1 end table$

Jadi nilai dari $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 plus 2 plus 3 plus... plus x over denominator begin display style 1 half x squared plus 1 end style end fraction end cell end table$ adalah