2. Money is deposited continuously at a constant rate of 1000 per year into a bank account that earns 5% interest compounded continuously, how many years will it take for the balance to reach $10,000 ?
3. a) Find the sum of the finite series 1/2³ - 1/2⁴ + 1/2⁵ - ... + 1/2¹⁵.
b) Determine whether the infinite series 1/2³ - 1/2⁴ + 1/2⁵ - ... + 1/2¹⁵ + ... converges, and if it converges find the sum it converges to.
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