1 + 1.2 1 1 n for all integers n>1 n+1 3. Prove that %3| 2.3 n(n+ 1)

Q: Verify that the following inequality is true for all integers n > 1 1 1.3.5. .... (2n 1) - 2n…

A:

Q: Find a Big-O estimate of (nn+n2n+3n)(n!+3n)

A: Consider the function fn=nn+n2n+3nn!+3n The objective is to give big-O estimate for the given…

Q: n3 + 3 n5 n4 - Prove that 14 + 24 + ..n* = +. n for all n > 1. 30 -

A: Consider the provided question,

Q: n! %3D if n is non-negative integer and proof r-1 r>t

A:

Q: For any integer n ≥ 1, C(6n, 3n) C(6n, 3n-1). O True O False

A:

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

A: Given statement:                           1+2.2+ 3.22+................+n. 2n-1  =  1+ (n-1). 2n…

Q: Show that the following claim holds when for all n > 1 n n(n + 1)(n +2) (+i) = 3 i=1

A: The aim is to show that ∑i=1n(i2+i)=nn+1n+23, for all n≥1. Consider the LHS, ∑i=1n(i2+i) and rewrite…

Q: For every positive integer n, 1 + 1.4 4.7 + ... + 1 (3n - 2)(3n+1) n = 3n+1

A:

Q: For every positive integer n     12+22+32+...+n2=n(n+1)(2n+1)/6 Let S(n)=12+22+32+...+n2 How do…

A: See the attachment

Q: Show that for all n ≥ 1, the n ₁²>(n+¹) " +1\ in

A: We have to show that for all n⩾1 , the inequality                  ∏j=1njj⩾n+12n(n+1)2Since…

Q: (a) Let n EN. Determine the set of all integers which leave a remainder n+1, n+2, n+3 when divided…

A: PART A As it is given that 2n+1, 2n+3, 2n+5 are consecutive odd integers so they are pairwise…

Q: Verify that the following inequality is true for all integers n > 1 · (2n – 1) 2.4.6.... (2n) 1…

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Q: Let n be an integer such that 1255 ≤ n and What is the smallest possible value of n satisfying the…

A: Given that, let n be an integer such that                                        and the value of n…

Q: Show that n 1 i2 i=1 <2 - n

A:

Q: Question 12 Which of the following is not correct? B n²(n+1)(n+2) 3 is 0 (n) for every integer n ≥ 3…

A: (A) n2n+1n+23 is θn4 for every integer n≥3     ∴n2n+1n+23=n2n1+1nn1+2n3=n431+1n1+2n=θn4 Hence option…

Q: X ME n! 3 11

A:

Q: 1(1!) + 2(2!) + ..+ n(n!) = (n + 1)! – 1. %3D 3.

A: (3) The given expression in the LHS can be written in the form of series as, ∑n=1nnn! Now solve the…

Q: or disprove : [nx] =n [x] %3D for all Positive integers n > 2

A:

Q: show that the general factorial function: () (¹) (+).. m (a)m here m is a positive integer and n is…

A: Given Data: To show that the general factorial function  αmn=mmnαmnα+1mn.........α+m-1mn here m is a…

Q: Prove that n Sk k=1 = n(n + 1)(2n + 1) 6 for all n € N.

A: To prove:We will use mathematical induction to prove this.Let

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

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

Q: n(n+1) for all n EN, • Given that 1+ 2 +3+..+n = the sum 70 + 71+72 + .+ 100 = 2

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Q: Find the largest number 8 such that 1 if 0 < r – 0.9| < S then <1.6. 0.92 8 =

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Q: Is 0.101001000100001000001… a repeating decimal? Is it rational or irrational? Explain (hint if the…

A: Explained below

Q: Σ >k· k! = (n + 1)! – 1 k=1 for every positive integer, n

A: We will prove this by principle of mathematical induction.

Q: (1+i)²n n! n=0 evaluate

A: The function ex has the expansion ex=∑n=0∞xnn!. The complex number eix=cos x+i sin x.  This is…

Q: Show that...

A: We have to show that: n1=nn-1 for n≥1. We know the formula, nr=Crn=n !r ! n-r ! Applying above…

Q: Determine all positive integers n > 3 for which is an integer. (n-1)n-1n² + 291 (n − 1) (n - 2)²

A: We have: simplified and expanded expressions.For the left side, we can expand using the binomial…

Q: Prove that 1-²-2+2-3- + + 1 n(n+1) = n n+1 for all n E N.

A: The given problem is to prove the given following identity,Given 1/1•2 + 1/2•3 + .. + 1/n(n+1) =…

Q: Show that for any integer n ≥ 2, C(2n,n) > C(2n,n-1)

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Q: Discrete Math

A: