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What is the sum of 1+3x+35x²/2 + 35⋅7x³/3! +...?

a) eˣ
b) cos(x)
c) sin(x)
d) 1/1−x



1 Answer

3 votes

Final answer:

The series in question resembles the power series expansion of eˣ; thus, its sum is eˣ.

Step-by-step explanation:

The series 1+3x+35x²/2 + 35·7x³/3! looks similar to the power series expansion of eˣ, where e is the base of the natural logarithm. By comparing it to the general formula for eˣ, which is eˣ = 1 + x + x²/2! + x³/3! + ..., we can see that the given series matches this form, with each term of the form 35ˣxⁿ/n! being multiplied by an extra coefficient of 35ˣ. Therefore, the sum of the series is simply eˣ.

User Te Ko
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