Prove that n² + 1> 2" when n is a positive integer with 1

Q: Prove that 6 divides n^3 − n whenever n is a non-negative integer

A:

Q: Show for all natural numbers n >= 3 that [(1 + (1/n))^n] < n.

A:

Q: 1+ 3n4" for every integer n ≥ 0.

A:

Q: सिद्ध है कि n! > 3 ^ n सभी पूर्णांकों के लिए n> = 7।

A: हमें दी गई समस्या को हल करना है:

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

A:

Q: Prove that if  n  is a positive integer, then  5 | (6^n − 1)

A:

Q: Prove that 6">5" + 9 for any integer n ≥ 2.

A: Mathematical induction is a technique used to prove statements about well-ordered sets of natural…

Q: Show that 2 + V5 is imational number

A:

Q: Find the number of positive integers not exceeding 100 that are either odd or the square of an…

A: The objective is to find the number of positive integers not exceeding that are either odd or the…

Q: Show that 3 + V5 is irrational number

A:

Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

Q: Show that (n + 1)! > 2"+3, for n > 5.

A:

Q: prove that Every positive integer n can be written as n =( 2^a)(5^b)c, where c is not divisible by 2…

A: Fundamental Theorem of Arithmetic: Every positive integer (except n=1) can be uniquely expressed as…

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

A:

Q: Show that n! > 3ª for n > 7.

A: The given inequality is, n!&gt;3n We need to prove that, the inequality is true for n≥7 Firstly,…

Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

Q: Prove that n-5 is odd iff n^2-1 is odd

A: Please check step 2 for the solution.

Q: Prove that n^2+5 >=4n for all integers, n>0.

A:

Q: Show that |x^n| = |x| ^n for every positive integer n and every real number x.

A:

Q: Prove that the sum of two consecutive positive odd numbers less than ten gives an even number

A: Given, The sum of two consecutive positive odd numbers less than ten gives an even number.  We have…

Q: Use proof by cases to show that if n is an integer then n^2 ≥ n.

A:

Statements and Logic

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