Consider the recursion X(n) = 2X(n-1) + 2 with the initial condition that of X(1) = 4. Using math induction prove that a closed-form solution to this recurrence is X(n)=2n +2n+1 – 2.

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.

its kinda hard to answer this when we dont have all the information that we need.

the argument of alfred t. mahan, henry cabot lodge, and albert j. beveridge was the economically and mass production the the americans could not consume themselves. this led expansion to sell to other foreign nations for profits.

step-by-step explanation:

this is my explanation