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Jumlah deret geometri tak hingga    adalah ....

Jumlah deret geometri tak hingga 

begin mathsize 14px style 2 plus square root of 2 plus 1 plus 1 half square root of 2 plus. space. space. end style 

adalah ....

  1. begin mathsize 14px style 4 square root of 2 end style 

  2. begin mathsize 14px style 2 minus square root of 2 end style 

  3. begin mathsize 14px style 2 plus square root of 2 end style 

  4. begin mathsize 14px style 4 minus 2 square root of 2 end style  

  5. begin mathsize 14px style 4 plus 2 square root of 2 end style 

Jawaban:

begin mathsize 14px style 2 plus square root of 2 plus 1 plus 1 half square root of 2 plus. space. space. equals ? a equals 2 r equals 1 half square root of 2 S subscript infinity equals fraction numerator a over denominator 1 minus r end fraction equals fraction numerator 2 over denominator 1 minus begin display style 1 half end style square root of 2 end fraction S subscript infinity equals fraction numerator 4 over denominator 2 minus square root of 2 end fraction equals fraction numerator 4 over denominator 2 minus square root of 2 end fraction times fraction numerator 2 plus square root of 2 over denominator 2 plus square root of 2 end fraction S infinity equals fraction numerator 4 open parentheses 2 plus square root of 2 close parentheses over denominator 4 minus 2 end fraction equals 2 open parentheses 2 plus square root of 2 close parentheses equals 4 plus 2 square root of 2 end style 

Jadi, jawaban yang tepat adalah E

 

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