Prove by mathmatical induction 1.2²+2.3²+3.4²+n(n+1)=n(n+1)(n+2)(3 n+5)/12

Last one and the bottom answer choice is y=(x-4)^2+1 you guys!

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?

Find cot x if sin x cot x csc x = √2