If we were writing an inductive proof for: if n is a positive integer, then Pn)-

Question

If we were writing an inductive proof for: if n is a positive integer, then Pn)-12+22 .n2. n0+ 12n+1) 6 Which of the following would be the inductive hypothesis? Assume that P(k + 1) is true for an arbitrary positive integer k, that is: P(n) = 12 + 22 + + k2 + (k + 1) (k+1)k +11)(2k1)+1) 6 Assume that P(k) is true for an arbitrary positive integer k, that is: Pk)- 12-22._... . K2. K(k+)2k+ 1) 6 Assume that P(1) is true k(k1)(2k+1) 6 P(k) is true, because k for an arbitrary positive integer k P(1) is true, because 1 6 O Assume that P(k) is true for an arbitrary integer k, that is: P-12+22D2k+1) 6

Explanation / Answer

The inductive hypothesis step in the proof by induction is the last step in the proof which is

Assume that p(k+1) is true for an arbitarary positive integer k that is

p(n)= 12+22+ ------+ k2 + (k+1)2 = (k+1)(k+1+1)(2(k+1)+1)/6 ,

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.