-Prove that a) b) n -("71) = (-+ 0 (," }) n r r+ n 2-0 (7) = 0 r=0

Q: Prove that (-1+ iE)" + (-1- i5" has either the velue 2n+! or the value -2" f ロ ww. š any integer…

A: The cube root of unity is written as:

Q: Which of the following is false? O ("2) = 2(") k ㅇ ") %3 (4") + (F) k n(n+1) (":"): 2 2 O ()² = (?)…

A: We have to check whether given statement is true or false.

Q: e3x e(n+1)x = 1+ e" + 2 enx Sx 6. n! (n + 1)!

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Q: prove : 1+1/(3)2+1/(5)2+1/(7)2+...=(pie)2/8

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Q: Show that 1+2+3+...+n= ("""). (";"').

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Q: If A = {r|- 23 < x < 3how many negative integers does Acontain? Note that: 'I' means 'Such that'

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Q: 6) If X is N(45,5) for i = 1, 2,..., 25; find: 25 (a) P (30 < (X-45) < 55) 221 b) P(30< (X -45) 2 <…

A: The objective of the question is to find the probability of two different scenarios for a normally…

Q: 5. (20) Prove by induction that for positive integers n, 4|(5"+1 + 32n-1).

A:

Q: 3. From Fermat's theorem deduce that, for any integer n 20, 13| 1112+6 + 1.

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Q: 11. (a) What does the symbol n! mean? Find 5!. (b) Define (), and find (2).

A: To find 5! and to find the value of 52

Q: Explain what this means in words (*:")- O()-O(-)--- 00 + m т +...+

A: In mathematics and statistics we use the terms permutations and combinations. When the…

Q: 5. (*) If a and b are nonzero integers such that a | b and b|a, prove that a = ±b.

A: .

Q: Find 1 (9) Lp(p – 1). p(p²-1)3 (10) L-1 (p2+1)2,

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Q: Show that /(-1)-7(1) but there is Let f(x) 1 Show that /(-1) (1) but there is no number e in (-1, 1)…

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Q: (- 1)" _ 3 En=0 'n =D0 3" 4 Select one: True O False

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Q: Seaet =1+ e* + e3x + e(n+1)x enx +esx. n! sx € (0,e*) | ... 2 (п + 1)!"

A: we know that ex=1+x+x22!+x33!+........................+xnn!                      ..1

Q: If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the following: %3D ) a-1 (a) In -12 b-3c-1 (b) In…

A:

Q: prove that (1- (1/4))(1-(1/9))(1-(1/16))...(1-(1/ n2)) =(n+1)/2n for all integers n greater than or…

A: We have to prove that  (1- (1/4))(1-(1/9))(1-(1/16))...(1-(1/ n2)) =(n+1)/2 By mathematical…

Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

A:

Q: Find a formula for +(−1)n. (2). 1 1 ¹ – ²2 ( ² ) + ² ( 2 ) - -· ··- 1 n+1

A: To Find: A formula for .

Q: Prove that 3! 2(n+3) = = n r=0 (-1) 1 n "Cr r+3 Cr

A:

Q: . Let n be a positive integer. Prove that 1 · ( n/ 1)  + 2 · ( n/ 2)  + . . . + n ·  (n/ n) …

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Q: integer of the form okts is also but not' conversely

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Q: Evaluate (1) − ² (17) + ³ (2) + - 2 ++ (-1)(n+1) n

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Q: Assume that M = N₁(h) + a₁h² + a₂hª + azh6 + ... Then using Richardson extrapolation N4 (h) is of…

A: Use Richardson's extrapolation formula for even power series, to obtain the solution.…

Q: How many zeroes are at the end of 1000!/(500!500!)?

A: Calculate number of zeroes in 1000! and then subtract it from the number of zeroes in (500!500!).

Q: For any positive integers m, n (

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Q: dx (1)(- 2e * )

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Q: Prove that 3! 2(n+3) = n r=0 (-1) n "Cr r+3 Cr

A:

Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

A:

Q: 5) For each + ive integer i, where i is equal to three, then find the union and intersection of…

A: 5 Given that Ai=x∈R|−1i&lt;x&lt;1i=−1i,1i. a We have to find the A1∪A2∪A3 and A1∩A2∩A3. Here,…

Q: Give a combinatorial proof for the identity 1+2+3+..+n= (",").

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Q: n —(2) - (-) (1)¹(1)(). (n-1)

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Q: (2) Give a proof by contradiction of theorem “If n^2+1is odd, then n is even”

A: The given problem is to prove by using the contradiction of Theorem of the given statement. Given…

Q: Show that:

A: Given, nr+nr+1=n+1r+1

Q: Prove or disprove the following statement: "For all real numbers x, y, [xy] = [x][y]." (3 marks)

A: Introduction: Two important functions are frequently used in mathematics and computer programming.…

Q: (п-1)! d) DE (x"-1nx)

A:

Q: 4. Prove that (À × B) · (B x T) × (T x A) = [ABT)

A: The objective is to prove that

Q: EC»(a-p)- = Ip + (1- p)" = 1" = 1.

A:

Q: Use substitution method to prove step-by-step that (PAQ)^(P = –(Q^R))^(S = R) = ¬S.

A: We are asked to prove the following using the substitution method, P∧Q∧P⇒~Q∧R∧S⇒R⇒~S We will show…

Q: 4. (**) Let [x] be the greatest integer that is ≤r. Then prove (10) IN [(k,n)

A: The idea of the problem is to use the definition of the greatest integer function.