Mathematics
Grade10
Easy

Question

Write the expansion of the series not stretchy sum subscript n equals 1 end subscript superscript 7 end superscript 3 open parentheses fraction numerator 2 over denominator 3 end fraction close parentheses to the power of n minus 1 end exponent.

  1. 8    
  2. 1 plus 9 plus fraction numerator 7 over denominator 8 end fraction plus fraction numerator 3 over denominator 2 end fraction    
  3. 3 plus 2 plus fraction numerator 4 over denominator 3 end fraction plus fraction numerator 8 over denominator 9 end fraction plus fraction numerator 16 over denominator 27 end fraction plus fraction numerator 32 over denominator 81 end fraction plus fraction numerator 64 over denominator 243 end fraction    
  4. 2 + 3    

hintHint:

The given is a recursive formula for a geometric progression with first term 3 and 2 over 3 as the common ratio

The correct answer is: 3 plus 2 plus fraction numerator 4 over denominator 3 end fraction plus fraction numerator 8 over denominator 9 end fraction plus fraction numerator 16 over denominator 27 end fraction plus fraction numerator 32 over denominator 81 end fraction plus fraction numerator 64 over denominator 243 end fraction


    The expansion of the given series is 3 plus 2 plus fraction numerator 4 over denominator 3 end fraction plus fraction numerator 8 over denominator 9 end fraction plus fraction numerator 16 over denominator 27 end fraction plus fraction numerator 32 over denominator 81 end fraction plus fraction numerator 64 over denominator 243 end fraction

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