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Series & Sequences (Standard)

Multi-step exam-style items.

Phase 2 · AP Calculus

FoundationsStandardAdvanced

Series & Sequences: core idea

nth-term test.

Example problem: hint and answer

Interval of ∑xn/n\sum x^n/n: right endpoint included? Type 11 yes 00 no for x=1x=1.

Hint: Harmonic at x=1x=1. Answer: 0.

Practice (9 problems — type your answers)

  • 1. Alternating harmonic ∑(−1)n+1/n\sum(-1)^{n+1}/n sum?

  • 2. Taylor T3T_3 for sin⁡x\sin x at 0: coefficient of x3x^3?

  • 3. Geometric sum ∑n=0∞(1/3)n\sum_{n=0}^{\infty}(1/3)^n?

  • 4. Ratio test on ∑n!/nn\sum n!/n^n: limit of ∣an+1/an∣|a_{n+1}/a_n|?

  • 5. Coefficient of x4x^4 in exe^x?

  • 6. Sum ∑n=1∞n/2n\sum_{n=1}^{\infty}n/2^n?

  • 7. p-series ∑1/np\sum 1/n^p converges for p>?p>? Enter threshold.

  • 8. Maclaurin of ln⁡(1+x)\ln(1+x): coefficient of x2x^2?

  • 9. Root test: lim sup⁡∣an∣1/n\limsup |a_n|^{1/n} for an=(1/2)na_n=(1/2)^n?

Series & Sequences Practice Problems — Standard