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

e^6+1/2

Solution

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

Some More Questions From Sequences and Series Chapter

For Daily Free Study Material Join wiredfaculty