InterviewSolution
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InterviewSolution
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The coefficient of `x^(10)` in the series of `e^(2x)` isA. `(2^(9))/(9!)`B. `(2^(10))/(10!)`C. `(1)/(10!)`D. none of these |
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Answer» Answer: We have `e^(x)=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)+…= underset(n=0)overset(infty)Sigma(2x)^(n)/(n!)` Replacing x by 2x we get `e^(2x)=1+(2x)/(1!)+(2x)^(2)/(2!)+(2x)^(3)/(3!)+….underset(n=0)overset(infty)Sigma(2x)^(n)/(n!)` Clearly `T_(n+1)=(n+1)^(th) term =(2x)^(n)/(n!)=(2^(n))/(n!)x^(n)` If `(n+1)^(th)` term contains `x^(10)` then we must have n =10 ltbvrgt `therefore` Coefficient of `x^(10)=(2^(10))/(10!)` |
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