Prove by mathematical induction

r(r+1)(r+2)= n/4 (n+1)(n+2)(n+3)

An initial investment of $100 is now valued at $150. the annual interest rate is 5%, compounded continuously. the equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. about how long has the money been invested? use your calculator and round to the nearest whole number. years

For f(x) = 3x+1 and g(x) = x2 - 6, find (g/f)(x)

Asquare and an equilateral triangle have the same perimeter. each side the triangle is 4 inches longer than each side of the square. what is the perimeter of the square