Use mathematical induction to prove the formula for all integers n ≥ 1. 1+ 4 + 7 + 10 + ... + (3n - 2) = (3-1) 2 Let S be the equation 1 +4+7+ 10 ++ (3n - 2) = (3n - 1). We will show that S is true for every integer n 2 1. n Select S, from the choices below. O 1+4= 5(2-1) = (3-1-1) 01+4=(3-3+ 1=(3-1-1) 2 = 1) Nice job! The selected statement is true because both sides of the equation equal Show that for each integer k ≥ 1, if Sk is true, then Sk + 1 is true. Assuming S is true, we have the following. (Simplify your answers completely.) Sk = 1+4+7+ 10 + ... + Then we have the following. (Simplify your answers completely.) 2)+(²([ 3 Sk+1=1+4+7+ 10 ++ (3k − 2) + = Sk + = - (3k-1) + +1)(1 (k+ 1) 2 k + 1 2 1)-¹) Hence, Sk + 1 is true, which completes the inductive step and the proof by mathematical induction

Q: (a) Prove by mathematical induction that the following statement is true for every positive integer…

A:

Q: 7n is a 15 n° Use mathematical induction to show that 5 3 natural number for all n E N. + +

A:

Q: n-(n+1)·(2n+1) 12 + 22 + 32 +... +n² ||

A: The solution is given as

Q: 1.50 Prove: 2+4+6++ 2n n(n+1) 1.51 Prove: 1+4+7+.+ 3n – 2 = n(3n-1) 1.52 Prove: 12 +22+32 + ... +n²…

A:

Q: Introduction to Descrete Mathematics  Show that for any n ∈ N, 6 | n 3 − n.

A: Given , a natural number n ,  Using the principle of mathematical induction we need to prove that  6…

Q: 12 + 22 + ..+n² = n(n+1)(2n+1) 6. is true?

A: Here we have to show that which value of n to proof the mathematical induction in the first step.

Q: 1.54 Prove: 5 + 39 + .+ 4n-3)4n+1) = 4n+I п 1-5 5.9 9.13 (4n–3)(4n+1) | 1.55 Prove 7" – 2" is…

A:

Q: use the Principle of Mathematical Induction to show that the given statement is true for all natural…

A: To Prove: 12+22+32+...+n2=nn+12n+16

Q: Prove the statement using induction. If n N, then (1-) (1-¹) (1-¹) (1-1)(1-2) +- 16 2n+1 3¹ +3² +3³…

A:

Q: 2 + 4 + 6 +...+ 2n = n(n + 1)

A:

Q: For ne N, 2n -8 < n²-8n + 17.

A: 3.7 We have to prove that 2n−8&lt;n2−8n+17 for all n∈N by principle of induction method. Let n=1…

Q: Using proof by induction

A:

Q: Explain why or why not the proof of the following result is correct or not correct. Let n be and…

A: We will explain why or why not the proof of the following result is correct or not correct.Let n be…

Q: xx+24=5x² fpyonbouy of anyos

A: We have xx+24≤5x2 Consider:…

Q: 11. a) Find a formula for 1 +... + 2" by examining the values of this expression for small values of…

A:

Q: Use mathematical induction to prove the following statement. n+1 ≥ 2₁ (1-2) (₁-3) (1 - ²2 ) -^21…

A:

Q: Use the permutation and combination formulas to prove the following. +k – 1) (n + k – 1 (b). V k, n…

A: We have to  prove given formula using peemutation and combination

Q: Prove the following statement by contradiction: If (n – 3)2 is an odd integer, then n is an even…

A:

Q: 47.) al Let n = P₁ P2... 92 the Prime factorization of n That a ak EN that is, ai 20) Positive…

A:

Q: Prove that n3 + 2n is divisible by 3 for all n E N.

A: We prove that n3+2n is divisible by 3 for all natural numbers n.

Q: "For all integers a, b and c, if a | b and b | c, then a | (5b – 3c)"

A: 4. Given the integers a, b and c. To prove: If a/b and b/c, then a/5b-3c.

Q: Prove 6n + 4 is divisible by 5 for all positive integers.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 1² +2²+3² 2 +...+ n² = n(n+1)(2n+1) 6

A:

Q: Fill in the blanks in the proof of the of fact that 3" – 1 is a multiple of 2 for every natural n.…

A:

Q: 1 + 3 + 5 +...+ (2n − 1) = n² -

A: Topic:- application of calculus

Q: Show that 3 is a factor of n3 + 2n for all natural numbers n. Let P denote the statement: 3 is a…

A:

Q: prove the statement is true by using Mathematical Induction.  1 + 2n &lt; 3n for all n ≥ 2

A:

Q: By the mathematical induction, n(n - 1)(2n - 1) is divisible by 6. False O True

A:

Q: 3 + 5 + 7+...+ (2n + 1) = n(n + 2)

A: Let the sum on the left hand side be Sn

Q: (Proof) For any integer n, n² + n is even.

A: We know the product of consecutive integers in a even integer.

Q: Prove that for every integer n where n is greater than or equal to 3, P(n+1, 3) - P(n, 3) = 3P(n,…

A: Given expression Formulas