Sequences and Series

Au programme

• What is the sum of the infinite geometric series 3 - 3/2 + 3/4 - 3/8 + ...?
• Which statement about the series Σ(n=1 to ∞) (-1)^(n+1)/n is correct?
• What is the radius of convergence of the power series Σ(n=0 to ∞) n!x^n?
• If a sequence is defined by a₁=2 and aₙ₊₁=3aₙ+2, which is its explicit formula?
• For the arithmetic sequence 7, 11, 15, 19, ... with indexing beginning at n=0, the nth term is [____].
• The sum of the first n positive odd integers, 1+3+5+...+(2n−1), is [____].
• The interval of convergence of the power series Σ(n=1 to ∞) xⁿ/n includes the endpoint x = [____] but excludes the…
• Given a₀=1 and aₙ=2aₙ₋₁+3, the explicit formula for the sequence is [____].