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Hitung jumlah kesepuluh dari deret-deret geometri berikut: b.

Hitung jumlah kesepuluh dari deret-deret geometri berikut:

b. begin mathsize 14px style 1 fourth plus 1 plus 4 plus horizontal ellipsis end style 

Jawaban:

begin mathsize 14px style 1 fourth plus 1 plus 4 plus horizontal ellipsis end style

Diketahui : 

begin mathsize 14px style a equals 1 fourth r equals U subscript 2 over U subscript 1 equals fraction numerator 1 over denominator begin display style 1 fourth end style end fraction equals 4 end style 

Ditanyakan: begin mathsize 14px style S subscript 10 ? end style 

Jawab:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell fraction numerator a open parentheses r to the power of n minus 1 close parentheses over denominator r minus 1 end fraction end cell row cell S subscript 10 end cell equals cell fraction numerator begin display style 1 fourth end style open parentheses 4 to the power of 10 minus 1 close parentheses over denominator 4 minus 1 end fraction end cell row blank equals cell fraction numerator begin display style 1 fourth open parentheses 1.048.576 minus 1 close parentheses end style over denominator 3 end fraction end cell row blank equals cell fraction numerator begin display style 1 fourth open parentheses 1.048.575 close parentheses end style over denominator 3 end fraction end cell row blank equals cell 1 fourth cross times 349.525 end cell row blank equals cell 87.381 1 fourth end cell end table end style 

Jadi, jumlah kesepuluh dari begin mathsize 14px style 1 fourth plus 1 plus 4 plus horizontal ellipsis end style adalah begin mathsize 14px style 87.381 1 fourth end style.

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