Q.7) In a party 25 people shake hands to each other (only once). How many n(n-1) handshakes will occur? ( Formula: 2

Q: (-1)" n+1 nEN. E = %3D n

A:

Q: 9. For the given formula write the type with order of the error term yI = yo +hf(xo, yo) Euler's…

A: Note : As per our guidelines we are supported to answer only first question

Q: What does Sn represent in the following formula: Sn:a(r^n-1)/r-1 Give 2 reasons why r ≠ 1.

A: In the given question Sn represents that

Q: B. Find e in the whole number. 1. N = 5,000 2. N = 20,000 3. N = 12,000 and n = 200 and n = 3,000 e…

A: B. Here we have to find e in whole number. Formula to calculate e is as,…

Q: 2 2/The third term of a geometric sequace whose First term 2 and its FiFth tom 162 is ? A- az a 18…

A:

Q: 1 5. of Colin's money is $43 more than - of Daniel's. If the two boys have $821 altogether, how much…

A:

Q: 4. Since a certain virus has been contained in Wakanda, researchers has proven that it will be…

A: The number of infected citizens, p thousand, after t weeks is given by…

Q: 2 Look at the following picture. 000 000 1st term 2nd term 3rd term Prove that the number of…

A: Given:

Q: Let floor(1) + floor(1/2) + floor(1/3) + …· + floor(1/n) = ceiling(0/1) + ceiling(1/2) +…

A:

Q: 3. Given n > 1, let S = E-1: Show that S, is not k=1 _k° an integer.

A: We are given that   Sn = ∑k=1n1/k   and n>1              ..(i) We have to show that Sn  is not an…

Q: Grandmother was born in 1942. a ni zodus In which year was she 70 years old? 21 29d a. mun b. How…

A: If the person is born in p year then the age of the person in q year is obtained by  required age…

Q: for all integers n >1 E, i = n(n+1} %3D 2

A: To prove the sum of n natural numbers n≥1 is  ∑i=1ni=n(n+1)2

Q: röve the following identity () - (":")- (:-) n n n | k k k 1

A:

Q: Show that for any n E N, 7(15".

A:

Q: n the diagram below, NOP similar WXY. Find each of the following:

A: Given figure,

Q: f in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n then prove that…

A:

Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

Q: Show that E [(X-µ)^n]=0 for ∀n, with X~N(µ, σ²) and n≥3 being odd numbers.

A: We need to show; E[(X-μ)n]=0 for ∀n and n≥3 being odd numberswhere;X~Normal(μ,σ2) That is, we need…

Q: If {an} is arithmetic, {bn} is geometric where r> 0. Given a = b1 = 2, b2 = a2, b3 = a2 + 4 Find an…

A: Here, given that an is an arithmetic sequence and bn is geometric sequence. And a1=b1=2. So,…

Q: 5. Given >U, = 3n(n +1) calculate the sum r=1 of ten terms starting from the eighth term.

A: Solution: Given that

Q: is equal to. k=1 n2 The sum O n+1 2n O n+1 O n? +1 2n2

A:

Q: 2. Let, a1= 3 and for n ≥ 2, an = 2an-1 + 1, express an in terms of n. for n ≥ 3, an = 2an-1+ bn-1…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: n°(r + 4)" 2 .n20/3 infinite, type "infinity" or 'inr".

A:

Q: 4. You are given: 7800-70t- 1? P30 0SIS TO 7800 Find qso-Hs0-

A: The given formula for tp30 represents the probability of an individual aged 30 years to survive the…

Q: 3. (3 pts) Find a counterexample that shows the following statement is FALSE: S: e*l < (n+1)° is…

A: We want to disprove the following statement by finding the counterexample. Sn: en+1&lt;(n+1)5  is…

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

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: 6. For the repeating decimal 0.4127, consider tne first 99 digits after the decimal point. Hlow many…

A: We are given the repeating decimal: 0.4127¯=0.412741274127......

Q: 8. If n+1, 2n-1 and n+5 are in AP. Find the value of n

A:

Q: [Hint: For m > 2, ( 2 7. For n > 1, verify that + 1 1² + 3² + 5² + ... + (2n – 1)° = ( 2"" ) - 8.…

A: Let's say we need to prove a formula or a statement P(n). To prove this, we need to prove that The…

Q: 24. There are seven finalists for the Math contest, and medals will be givền tổ thể tốp many ways…

A: Permutation:   It is nothing but the arrangement of items in a definite order where the order is…

Q: 6) If nP3 = 2 nC4 then nC6 = A. 1716 B. 3003 noituloa s ni fluash blud C. 5005 D. 8008

A:

Q: Given that P= (ad), 428 Engineering Mathematics where a +d=-1 and ad-be = 1, show that and hence…

A: Given Problem:- p=abcd Given a+d=-1 and ad-bc=1 Show that  p2=d-b-ca Hence deduce that  p2+p+1=0

Q: Example 11. Insert A.M.s between 7 and 71 in such a way that the 5th A.M. is 27. Find the number of…

A:

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

Q: 1. Prove that the sum of the consecutive cubes is given by this formula: n²(n+1) 4 13 + 23 + 33 +..+…

A: Given; 1) 13+23+33+...+n3=n2(n+1)2/4 Repost the next questions.

Q: 1/2% of $800 is $?

A: the given question is from the percentage and we have to find the half percent of the $800 is what…

Q: 7) For n copies of the book Me and My Sasquatch, a print-on-demand company charges C(n) dollars,…

A: Explanation: The given cost function is: a)  Here we need to find the C(20). Check each piece of…

Q: Given: 21 = 2 23 = L4 e || n Prove: 2 3

A: …

Q: Find a formula for Sn, n > 1, if sn is given by 6 7 3' 5' 7' 9' 11 4 8 - Sn =

A:

Q: Vn EZ, if n+5 is odd then n is even

A: This question is related to integer values. We can prove it by using direct or indirect way. Please…

Q: 7. Find k so that dx ke + C.

A:

Q: The number N of deer in a certain population t years after observation began is given by  N =…

A: Given: The number N of deer in a certain population t years is To find: The deer population after…

Q: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: 2. Taylor notes the odometer on their car reads 49,996 at the beginning of their day. When they…

A: Theorem of function based on continuous. Odometer is continuous reading of distance.

Q: -6an-1 for n > 2 with the initial condition a = -9. an an

A: Given an = -6an-1

Q: Use Gauss’s trick to determine H(n) = 1 + 5 + 9 + 13 + … + (4n – 7) + (4n – 3) + (4n + 1) I'm…

A: Explained below

Q: Suppose the final score in a hockey game is 4 to 2. How many possible scores are there after the 1st…

A: Team one had 5 different possible score total at the end of the 2nd {0,1,2,3,4} Team two had 3…

Q: 2n2 – 4n +1 is even → n is odd

A:

Q: 6n_ and If (ar + bx) = n+1 k-1 , then 1 (ak – br) = 712 n+2 k-1 k-1

A: If ∑k=1nak+bk=6nn+1 .......................(1)  and  ∑k=1nak-bk=nn+2-1n ......................(2) we…