We cannot use Mathematical Induction to make recursive deﬁnitions. True or False?

Question

Question

We cannot use Mathematical Induction to make recursive deﬁnitions.

True or False?

math Advanced-Math

Answer 1

Answer #1

False.

For example , suppose the the recursive relation a_n is defined by ,

a_n = a_n-1 + n and a₁ = 1

We can use induction on n to prove that ,

a_n = $\frac{1}{2}n (n +1)$ .

So false.

Answer 2

Similar Homework Help Questions

please use the principle of mathematical induction to show that the statement is true for all...

please use the principle of mathematical induction to show that the statement is true for all natural numbers please show both conditions 2+6+ 18 + ... +2.3n-1 = 37 - 1
how do I prove this by assuming true for K and then proving for k+1 Use mathematical induction to prove that 2"-...

how do I prove this by assuming true for K and then proving for k+1 Use mathematical induction to prove that 2"-1< n! for all natural numbers n. Use mathematical induction to prove that 2"-1
Use mathematical induction to prove that the statement is true for every positive integer n. 5n(n...

Use mathematical induction to prove that the statement is true for every positive integer n. 5n(n + 1) 5 + 10 + 15 +...+5n = 2

QUESTION 3 Show all your work on mathematical induction proofs Use mathematical induction to prove the...

QUESTION 3 Show all your work on mathematical induction proofs Use mathematical induction to prove the formula for every positive integer n
Use the Principle of mathematical induction to prove 2. Use the Principle of Mathematical Induction to...

Use the Principle of mathematical induction to prove 2. Use the Principle of Mathematical Induction to prove: Lemma. Let n E N with n > 2, and let al, aa-.., an E Z all be nonzero. If gcd(ai ,aj) = 1 for all i fj, then gcd(aia2an-1,an)1. 1, a2,, an
Use principle of Mathematical Induction show statement is true for all natural nunbers n 2+6+ 18+...

Use principle of Mathematical Induction show statement is true for all natural nunbers n 2+6+ 18+ ... +2.3n-1 = 3 - 1

Use mathematical induction to prove that the statements are true for every positive integer n. 1...

Use mathematical induction to prove that the statements are true for every positive integer n. 1 + [x. 2 - (x - 1)] + [ x3 - (1 - 1)] + ... + x n - (x - 1)] n[Xn - (x - 2)] 2 where x is any integer 2 1
Using Induction and Pascal's Identity Using Mathematical Induction Use induction and Pascal's identity to prove that...

Using Induction and Pascal's Identity Using Mathematical Induction Use induction and Pascal's identity to prove that () -2 nzo и n where
Question 3 Use mathematical induction to prove 3 + 7 + 11 +. + (4n -...

Question 3 Use mathematical induction to prove 3 + 7 + 11 +. + (4n - 1) = n (2n + 1). Show P1 is true. Assume Pk is true. Show Pk11 is true.

Discrete math show all work please Use mathematical induction to prove that the statements are true...

Discrete math show all work please Use mathematical induction to prove that the statements are true for every positive integer n. n[xn - (x - 2)] 1 + [x2 - (x - 1)] + [x:3 - (x - 1)] + ... + x n - (x - 1)] = 2 where x is any integer = 1