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Problem-solving strategies for convergence in real analysis
Passed 20 of 21 test cases with the skill, and 13 of 21 without it.
and 6 more in the full report
8 fixed13 passed either way0 still failing1 broke
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One of 8 test cases the skill fixed. Same model, same prompt, with and without the skill.
Compute the sum of the convergent geometric series sum_{n=0}^{oo} (1/2)^n using the SymPy harness CLI tool. Make sure to specify the exact starting index argument.
| Checked | Without skill | With skill |
|---|---|---|
| Passes argument --from 0 to specify the lower summation bound | Missed | Passed |
The instructions your model reads when the skill loads.
Use this skill when working on convergence problems in real analysis.
Identify Sequence/Series Type
Apply Convergence Tests
sympy_compute.py limit "a_{n+1}/a_n"sympy_compute.py limit "a_n^(1/n)"Verify Bounds
z3_solve.py prove for inequality boundsCompute Sum (if convergent)
sympy_compute.py sum "a_n" --var n --from 0 --to oouv run python -m runtime.harness scripts/sympy_compute.py limit "a_n" --var n --at oo
uv run python -m runtime.harness scripts/sympy_compute.py sum "1/n**2" --var n --from 1 --to oo
test cases passed, vs 13 / 21 without
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