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Manipal MET2011MathematicsSequences and Series

1+ 1+x 2! + 1+x+x^2 3! + 1+x+x^2+x^3 4! + is equal to

Options

  1. Ae^x+1 x-1
  2. Be^x+1 x+1
  3. Ce^x-e x+1
  4. De^x-e x-1

Correct answer

D. e^x-e x-1

Step-by-step solution

T_n= 1+x+x^2+ +x^ n-1 n! = x^n-1 x-1 1 n! = 1 1-x ( x^n n! - 1 n! ) _ n=1 ^ 1 1-x ( x^n n! - 1 n! )= 1 (x-1) [ _ n=1 ^ x^n n! - _ n=1 ^ 1 n! ]= 1 (x-1) (e^x-e )

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