# Calculus Problems

## Question

1. A water tank is in the form of a upper cone with height 20 meters and radius 6 meters. If the tank is half full of water, find the work required to pump all of it over the top rim. (water mass density is 1000 kg/m³)

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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