1. The problem is to analyze the given series and understand its behavior and graph. 2. The series is: $$1 + \frac{3}{7}x + \frac{3 \times 6}{7 \times 10}x^2 + \frac{3 \times 6 \times 9}{7 \times 10 \times 13}x^3 + \cdots$$ 3. Notice the pattern in the coefficients: numerator terms increase by 3 each time (3, 6, 9, ...), and denominator terms increase by 3 each time (7, 10, 13, ...). 4. This is a generalized hypergeometric-type series with terms: $$a_n = \frac{3 \times 6 \times 9 \times \cdots}{7 \times 10 \times 13 \times \cdots} x^n$$ 5. The graph described is a smooth blue curve with a green-shaded area under it from $x=0$ to about $x=2.6$. 6. The function represented by the series can be approximated or recognized as a special function, but here we focus on the series and its partial sums. 7. The series converges for values of $x$ within a certain radius, and the graph shows the function behavior in the range $-1$ to $3$ on the x-axis. 8. The green-shaded area under the curve from $0$ to $2.6$ represents the definite integral of the function over that interval. Final answer: The series defines a smooth function with the given coefficients, and the graph illustrates its behavior and integral area between $x=0$ and $x \approx 2.6$.