Prove the following formulas by mathematical induction. For each solution, please specify your (1) basecase; (2) induction hypothesis; and (3) the inductive step. For all n ∈ Z+:

n
Σ 1/i(i+1) = n/n+1
i=1

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?