Problem Analysis #5

Kanana-2-30B-Thinking · Run 1

23.50s
5,629 toks
Problem Statement

Let ([0,2],B([0,2]),λ)( [0,2], \mathcal{B}([0,2]), \lambda ) be the Lebesgue measure space. \nFor each n∈Nn \in \mathbb{N} define

:=∑k=1n2123456(x2) k−1(1−x2)3,x∈[0,2].:= \sum_{k=1}^{n^2} 123456 \left(\frac{x}{2}\right)^{\,k-1} \left( 1 - \frac{x}{2} \right)^{3}, \qquad x \in [0,2].

\nCompute the value

Ground Truth
82304
Execution Trace
Reasoning Process

[THOUGHT] I will compute the exact value of the limit by algebraic manipulation. The expression inside the integral simplifies to a geometric series, and the limit can be evaluated by recognizing that the term involving n tends to zero. The final value is 123456 multiplied by 2/3. [/THOUGHT] [PYTHON] print(123456 * 2 // 3) [/PYTHON]

Tool Output
[PYTHON OUTPUT] 82304 [/PYTHON OUTPUT]
Reasoning Process

[THOUGHT] The Python code computed 123456 multiplied by 2 divided by 3, resulting in 82304. This matches the analytical solution where the limit evaluates to 123456×23=82304123456 \times \frac{2}{3} = 82304.

82304\boxed{82304}

Final Model Output
82304

Comparative Analysis (P5) (Average across runs)

Avg Time Taken

Solar-Open-100B
550.5
Gemini-3-Pro-Preview
42.3
Kanana-2-30B-Thinking
38.5
HCX-007
34.1
GLM-4.5-Air
31.7
K-EXAONE-236B-A23B
29.5
Kanana-2-30B-Thinking-2601
21.1
Solar-Pro 2
19.7
GPT-5.2 (high)
13.1
EXAONE-4.0-32B
6.5

Avg Token Usage

Solar-Open-100B
17025.7
Kanana-2-30B-Thinking
9881.7
Kanana-2-30B-Thinking-2601
6458.3
GLM-4.5-Air
5912.0
Gemini-3-Pro-Preview
5738.7
Solar-Pro 2
5609.7
HCX-007
4853.7
K-EXAONE-236B-A23B
4492.3
EXAONE-4.0-32B
4188.3
GPT-5.2 (high)
3264.0