Final answer:
To find the sum of the given power series p1(x) and p2(x), simply add the corresponding terms to get the combined series: 2 + 10x + 58x² + 370x³ + 2482x⁴.
Step-by-step explanation:
The question asks us to add the first five terms of two given power series p1(x) and p2(x) to find their combined series. The given series are:
p1(x) = 1 + 7x + 49x² + 343x³ + 2401x⁴ + ...
p2(x) = 1 + 3x + 9x² + 27x³ + 81x⁴ + ...
To find the first five terms of p1(x) + p2(x), we simply add the corresponding terms:
- (1 + 1) = 2
- (7x + 3x) = 10x
- (49x² + 9x²) = 58x²
- (343x³ + 27x³) = 370x³
- (2401x⁴ + 81x⁴) = 2482x⁴
Therefore, the first five terms of p1(x) + p2(x) are 2 + 10x + 58x² + 370x³ + 2482x⁴.