rove that n n² + 1 < 1 n for all n E N.

Q: Let = n n i=1 x₁ . Then for constants a and b, n Σ a(x₁ - ī) b² =? (6²5m)

A: The question is about parametric inference.Given :Where,X1, X2, ...., Xn are independent random…

Q: A sequence is said to be decreasing sequence if Vn > 1 'n+1°n =S .a .b O n+1 2n.cO n+1 n+1d0 n

A: Option (d) is correct.

Q: n 2n + 2 /2 n 2n k k=1 \k –1, п+1 n -

A: The objective is to prove that ∑k=1nnknk-1=2n+2n+1/2-2nn This theorem can be proved by induction,…

Q: alc and b|c, then ab|c if a and b are not relatively prime.

A: The given statement is FALSE. Given a|c and b|c then ab|c if a and b are not relatively prime. If…

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

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

A:

Q: 2. Show that 7-(4-3 k=0 (-1) k + 1 \k n+1

A:

Q: 4. Conclude that n2 n=1 ||

A:

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: Q5 Show that EL >². n n =1

A: Consider that x is a random variable. From the formula of population variance;

Q: n (n + () A k=0 | B, = 0.

A:

Q: Find the value of  n! (n − r)!r!  when n = 6 and r = 4.

A:

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: Wht is the sum of this 8.1 - 3.1 x 2.1 + 0.4

A:

Q: each st

A: The equation is given as 8+3|2x−11|&gt;1. Subtract 8 from both sides. 3|2x−11|&gt;-7 Divide by 3.…

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

A:

Q: (1.2) Show that m m+n+1] m k=0 for any two positive integers m and n.

A: Please check the next step for detailed answer.

Q: Solve for n. k (3-n) %3D

A: b=k(3-n)pbp=k(3-n)

Q: Let n = WEE 5 Find n - 1. n – 1 =

A: Given:- n=-2/5 To find:- Value of n-1

Q: Indicate the smallest integer n such that (6x²+4x)³ f(x) = € 0(x¹). 2A-4x On=4 O n=2 O n=1 O n=6 O…

A: f(x) = (6x2 + 4x)3/(x4 - 4x)         = {2x(3x + 2)}3/{x(x3 - 4)}        = 8x3(3x + 2)3/{x(x3 - 4)}…

Q: Show the solution that a,+1 < a, for each n E N (-1)" п! n=1

A: Find your answer below

Q: X ME n! 3 11

A:

Q: n(n+1) For all n E N, prove 1 + 2 + ··· + n = 2

A:

Q: (3x* – 1) dx + x°dy = 0; when x = 1, y = 1

A:

Q: all n N we have We apply this successively for n = bn+1 bn N, N+1, n 9 bN+1 < (m + €)bN bN+2 < (m+…

A:

Q: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: n(n + 1)(2n + 1) 6 k=0

A: In this question, we prove the sum of squares of natural numbers.