Let P (n) be the statement that 1³ + 2³ + · · · + n³ = (n(n + 1)/2)² for the positive integer n. a) What is the statement P (1)? b) Show that P (1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis. f ) Explain why these steps show that this formula is true whenever n is a positive integer.

14

step-by-step explanation:

14 x 3 = 42

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

6x = 48

i hope this . 6 cards each and a total of $48. dvide each side by 6 and you will have your answer.