Prove that 2 - 2 · 7 + 2 · 72 – ... + 2(-7)" = (1 – (-7)n+1)/4 whenever n is a nonnegative integer.

Q: Prove that 1– 2+2² – 2° + -.-+(-1)"2"=2**1 for all nonnegative integers n.

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Q: Prove that 3"< n! whenever n is a positive integer greater than 6.

A: Here we are to prove 3n&lt;n ! whenever n is a positiveinteger greater than 6.To solve this problem…

Q: Prove that for every non-negative integer n the value of n² + n+41 is prime ?

A: The number n² + n + 41 is not prime for every natural number n. Let, f(n) = n² + n + 41

Q: Prove that if n is an integer and 3n + 2 is even, then n is even using a) a proof by contradiction.

A: Given: 3n + 2 is an even integer Let n is not even, thus n is odd. Therefore, by using the…

Q: Prove or disprove: For every positive integer n, 22n – 1 is divisible by 3. -

A: I have proved the result using mathematical induction

Q: Prove that 1/(2n) < [1 · 3 · 5 . ... · (2n – 1)]/(2 · 4 · .. 2n) whenever n is a positive integer.

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Q: Prove that 3n<n! if n is an integer greater than 6

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Q: Prove that 25|(6" – 5n – 1) for all positive integers n. -

A: We can prove given statement by principle of mathematical induction: Alogrithm: Obtain P(n) and…

Q: ) Prove every integer n >= 7, n! > 3n

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Q: Prove that 2n+1 +(-1)" 3-2 whenever n is a nonnegative integer.

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Q: Prove that the statement is true for every positive integer n.

A: Given arithmetic progression (AP) is: 2+5+8+.........+3n-1 Here the first term is 2 and the common…

Q: 3. Prove that if n is an odd integer then 7n+5 is even.

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Q: prove that 2. 3+3.5+ 3.5 3.5^= 3(s^) 3.S+.+3.5" %3D 4 whenever is a nonnegative integer

A:

Q: Prove that the statement is true for every positive integer n.

A: Given,  2+7+12+...+(5n-3)=12n(5n-1)

Q: Prove or disprove: 2n + 1 is prime for all nonnegative integers n.

A: Prove or disprove: 2n + 1 is prime for all nonnegative integers n.

Q: Prove that n2 – 7n + 12 is nonnegative whenever n is an integer with n > 3.

A:

Q: 2. Prove by induction (n+1) (n+2) - 1 is odd for all positive numbers of n >= 0

A:

Q: 32. Prove that 3 divides n + 2n whenever n is a positive integer.

A:

Q: Prove that n(n + 1)(2n + 1) (3n2 + 3n - 1) 30 whenever n is a positive integer.

A: see below attached explanation

Q: Prove that n- + 1> 2" when n is a positive integer with 1 <n<4.

A:

Q: Prove that 3 | 22n+1 +1 for all natural numbers n.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Prove that 12 +32 +52 + ...+ (2n + 1)? = (n + 1) (2n + 1)(2n + 3)/3 whenever n is a nonnegative…

A: To prove: That 12+32+52+...+2n+12=n+12n+12n+33 where, n is non negative number. Calculation: Use…

Q: Use mathematical induction to prove that 12 + 32 + 52 + .…+ (2n + 1)² = (n+1)(2n+1)(2n+3) where is a…

A: We need to prove the given result by mathematical induction. The solution is as follows.

Q: Q1 Use mathematical induction to prove that (-5)"+1 – 1 3 + 3 * (-5) + 3 * (-5)² + 3 * (-5)³ + .… +…

A: Given equation is, 3+3(-5)+3(-5)2+3(-5)3+......+3(-5)n=(-5)n+1-1-2

Q: Use indirect proof to show that if n is an integer and n^3 + 5 is odd, then n is even.

A:

Q: Let n be a positive integer. Prove that :)- (:)- +2. +...+n. = n2"-1

A: Binomial Theorem: According to the binomial theorem, let x and y are any two numbers. Then it is…

Q: (3n)! is an integer for all n > 0. (3!)n Prove that

A: We will prove it by Mathematical induction. First We show it is true for initial condition n=0…

Q: 6. Prove that 3" < n! whenever n is a positive integer greater than 6.

A: We need to prove that ,  3n &lt; n!  for every positive integer n greater than 6. We will use method…

Q: Prove that ifnis an integer and3n+ 2is even, thennis even using a proof by contraposition.

A: Contra-positive: "If q then p" is the contra-positive of a conditional statement of the type "If p…

Q: show that no integer of the form n^3+1 is a prime other than 2

A:

Q: Prove or disprove that for every positive integer n, if n is even then n^{2}+1 is prime.

A: False

Q: Prove that the statement is true for every positive integer n.

A: Prove that the statement is true for every positive integer n. 22+42+62+...+2n2=2n2n+1n+13 We prove…

Q: Prove that 12 + 32 +52 +...+ (2n + 1)2 = (n + 1) (2n + 1)(2n + 3)/3 whenever n is a nonnegative…

A: The sum of the square of odd numbers can be written as, ∑k=0n(2k+1)2 Now expand the expression under…

Q: Prove that 2n>n2 if n is an integer greater than 4.

A: According to the given information, it is required to prove the given statement.

Q: Prove that the statement is true for every positive integer n.

A: Given, Prove this statement is true for every positive integer n: 2+4+6+..+2n=n(n+1)

Q: Prove that n2 +1 > 2? when n is a positive integer with 1<n<4.

A:

Q: Prove that 2n + 3 ≤ 2n if n is an integer greater than 3.

A: Sol :- To prove:- 2n+3&lt;=2^n if n is an integer greater than 3 We prove this by induction For n=4…

Q: Prove that 12+3² + 5² + . . + (2n + 1)² = (n + 1) (2n + 1)(2n +3)/3 whenever n is a nonnegative…

A:

Q: Prove that 12+32 +5² + ..+ (2n + 1)² = (n + 1) (2n + 1)(2n +3)/3 whenever n is a nonnegative…

A: We know, 12+22+32+42+ . . . +n2=nn+12n+16 Therefore, 12+22+32+42+ . . . +2n+12=2n+12n+24n+36 Now,…

Q: prove that there is no positive integer n such that n^2+n# = 100

A: n^2+n^3 = 100 We can evaluate this till some positive integers

Q: Prove 8^ +l is composic for any poSitive integer n.

A:

Q: 2. Prove that if 2n² + 7n is even and n is an integer, then n is even.

A: We have to prove that the given statement is true by the help of mathematical induction

Q: Prove that for every non-negative integer n the value of n^2+n+41 is prime

A:

Q: Prove that n² + 1> 2" when n is a positive integer with 1<n<4.

A: Given: is a positive integer with. To prove: .

Q: Prove that 1- 1! +2 · 2! + .. +n ·n! = (n+ 1)! – 1 whenever n is a positive integer.

A:

Q: Prove that n^2 is an even number if and only if 3n + 1 is an odd number by proving  If n^2 is even…

A:

Q: Give a contrapositive proof of the theorem  If n is an integer and 3n+2 is even ,then n is even

A: We have to prove given statement by contrapositive proof.

Q: prove that n^2 +1 >= 2^n when is a positive integer with 1<=n<=4

A: To prove n^2 +1 &gt;= 2^n when is a positive integer with 1&lt;=n&lt;=4

Q: Prove by induction that (2) = n22"+1 – n2"+2 +3.27+1 - 6 whenever n is a positive integer

A:

Q: Prove by induction that the product of the first n even numbers is equal to n!2" for all positive…

A: We have to prove by induction that the product of first n even numbersis equal to n!2n for all…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.