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.