4. Conclude that n2 n=1 ||

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: n 21. if an+1 = an an 2n + 3 n=1

A: We have, an+1=n2n+3an Substitute value of n=0,1,2,3,4,..... At n=0, a1=020+3a0a1=0 At n=1,…

Q: 3n > n for every positive integer n.

A: Now, since we assumed 3k>k, we can substitute k with 3k in the inequality: 3k+1>3k Since ,…

Q: calculate 1+3+5+...+(2n-1) for n = 1,2...,6.

A:

Q: Integrate: / 82

A: Given integration is : ∫8x3lnxdx  To find the value of integration.

Q: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: . Show that n! > 3ª for n> 7.

A:

Q: a. 3.2F> Fn+1 for n23 [Solutions and final ans

A: We need to prove 2Fn>Fn+1 Now, we have formula for fibonacci sequence is Fn=Fn-1+Fn-2

Q: Show that (n) ‡ 14 for all n ≥ 1.

A:

Q: Prove that (A-1)-1 = A. %3|

A: Let A be inverse of matrix A. Then, by definition We know that

Q: Prove that 2n + 3n is a multiple of 5 for all odd n € N.

A:

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

A:

Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

A:

Q: P show that (α) |=1 = 12/

A: A detailed solution is given below.

Q: Find all positive integers n such that 2" – 1 | 3" – 1. - -

A: Given 2n-1|3n-1 ,  for n∈ℤ+ To find if the statement is true.

Q: 1. Prove that (fn+1fn+3 – fnfn+4)* = 4 for each positive integer n.

A: We need to prove this, fn+1fn+3-fnfn+42=4

Q: | (16 – 2*) dz =

A: To find : the value of ∫0216-x4dx   Using the formula ∫abxndx=1n+1bn+1-an+1

Q: . n &gt; 5 only if n &gt; 7.

A: Given that n&gt;5 only if n&gt;7

Q: that if 3 divides the sum of the digits of n, then 3|n

A:

Q: For which values of n does n! have n or fewer digits

A: Solution is as follows

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: 4. Find the first three terms of (3x – 2)20. What is the coefficient of æ10?

A:

Q: Evaluate |P(A)| if A={n: n is a prime number from 1 to 100}

A: To evaluate : PA if A=n : n is a prime number from 1 to 100

Q: an (b) Explain what it means to say that n=1

A: According to question,Given expression,∑n=1∞an = 12

Q: Show that. 1 (n + 1)(n + 2) n=1

A:

Q: c). |M||N| (M + N)

A: Given problem:- Given the vectors  M = -12ax + 3ay – 8az  N= 8ax + 5ay – 2az. find the |M||N|(M+N)

Q: Find L (3 + e")*] 1 s-6 s-12 9. 1 s-6 s-12 1 s+6 s-12 o 9 6. 1 s-6 s-12 6/9

A:

Q: Show that 5 | n5-n for all integers n.

A: To prove the above statement we will use the principle of mathematical induction which is divided in…

Q: B={z|z is a integer and -2&lt;Z&lt;0}

A: Given,

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.