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Sequences And Series

Question
CBSEENMA11015595

The sum of the series fraction numerator 1 over denominator 2 space factorial space end fraction minus fraction numerator 1 over denominator 3 factorial end fraction space plus space fraction numerator 1 over denominator 4 factorial end fraction space..... space upto space infinity

  • e-2

  • e–1

  • e-1/2

  • e6+1/2

Solution

B.

e–1

straight e to the power of straight x space equals 1 minus straight x space plus space fraction numerator straight x squared over denominator 2 factorial end fraction space minus space fraction numerator straight x cubed over denominator 2 factorial end fraction space plus space fraction numerator straight x cubed over denominator 3 factorial end fraction space plus fraction numerator straight x to the power of 4 over denominator 4 factorial end fraction minus.....
put space straight x space equals space 1
fraction numerator 1 over denominator 2 factorial end fraction space minus fraction numerator 1 over denominator 3 factorial end fraction space plus fraction numerator 1 over denominator 4 factorial end fraction space...... space equals straight e to the power of negative 1 end exponent