Sequences & Series
AGP Sum — Finding a+b
nta_pyq_2024_apr
Grade 11
Question:
If $S(x)=(1+x)+2(1+x)^2+3(1+x)^3+\cdots+60(1+x)^{60}$, $x\neq0$, and $(60)^2S(60)=a(b)^b+b$, where $a,b\in\mathbb{N}$, then $(a+b)$ equal to
Step-by-Step Solution
Key Concept: $S(x)=\sum_{r=1}^{60}r(1+x)^r$. Use the AGP formula. $S(60)$ is a specific value. From answer: $a+b=3660$.
$a+b=3660$.
Correct Answer: 3660