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If H subscript n end subscript equals 1 plus fraction numerator 1 over denominator 2 end fraction plus horizontal ellipsis plus fraction numerator 1 over denominator n end fraction, then value of S subscript n end subscript equals 1 plus fraction numerator 3 over denominator 2 end fraction plus fraction numerator 5 over denominator 3 end fraction plus horizontal ellipsis plus fraction numerator 99 over denominator 50 end fraction is

  1. H subscript 50 end subscript plus 50   
  2. 100 minus H subscript 50 end subscript   
  3. 49 plus H subscript 50 end subscript   
  4. H subscript 50 end subscript plus 100  

The correct answer is: 100 minus H subscript 50 end subscript


    S subscript n end subscript equals 1 plus fraction numerator 3 over denominator 2 end fraction plus fraction numerator 5 over denominator 3 end fraction plus horizontal ellipsis plus fraction numerator 99 over denominator 50 end fraction
    equals open parentheses 2 minus 1 close parentheses plus open parentheses 2 minus fraction numerator 1 over denominator 2 end fraction close parentheses plus open parentheses 2 minus fraction numerator 1 over denominator 3 end fraction close parentheses plus horizontal ellipsis plus open parentheses 2 minus fraction numerator 1 over denominator 50 end fraction close parentheses
    equals 100 minus H subscript 50 end subscript

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