If (e^{x} = 1 + x + frac{x^{2}}{1.2} + frac{x^{3}}{1.2.3} + … ), find (frac{1}{e^{frac{1}{2}}})
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A.
1 – (frac{x}{2}) + (frac{x^2}{1.2^3}) + (frac{x^3}{2^4.3}) + ……… -
B.
1 – (frac{x}{2}) + (frac{x^2}{1.2^3}) + (frac{x^4}{2.4.3}) + .. -
C.
1 + (frac{x}{2}) + (frac{x^2}{1.2}) + (frac{x^3}{1.2.3}) + (frac{x^4}{1.23.4}) + ……… -
D.
1 – x + (frac{x^2}{1.2^3}) + (frac{x^3}{2^4.3}) + ……… -
E.
1 + (frac{x}{2}) + (frac{x^2}{1.2^3}) + (frac{x^4}{1.2.6}) + ………
Correct Answer: Option C
Explanation
(e^{x} = 1 + x + frac{x^{2}}{1.2} + frac{x^{3}}{1.2.3} + …)
(frac{1}{e^{frac{1}{2}}} = e^{-frac{1}{2}})
(e^{-frac{1}{2}} = 1 – frac{x}{2} + frac{x^{2}}{1.2^{3}} – frac{x^{3}}{1.2^{4}.3} + … )