If a₁, 92, ..., a, are in arithmetic progression, where a; > 0 for all i, then show that √a₁ 1 1 1 + √a₂ + √a₂ + √az ++ √an-1 + n-1 √a₁ + √an √an

Q: Letting aa and bb be two positive real numbes such that ab=lab=1, which of the followings is true?…

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Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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Q: Show that An, n > 5 is simple.

A: Sol:- To show that An, the alternating group of even permutations of degree n, is simple for n ≥ 5,…

Q: A={3,8,11,14,21} |A×{5}|(please think carefully before doing this)

A: Given....

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

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Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

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Q: For some real numbers m and n, the list 3n2, m2, 2(n + 1)2 consists of three consecutive integers…

A: For some real numbers m and n, the list 3n2 ,  m2  , 2(n + 1)2  consists of three consecutive…

Q: Find integers ? and ? such that 3220? + 6006? = gcd(3220,6006).

A: Remark: The greatest common divisor (gcd) of two integers is the greatest integer that divides both…

Q: so-Z of what is 21

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Q: Find all integers n such that n| (2n+3). *

A: Given, n|(2n+3)     TO find, All integers n

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

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Q: Let Find formulas for the entries of M", where n is a positive integer. Hint: a formula such as 5…

A: Given that the matrixM=16-147-5

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Q: let a and b be integers, if 7|(17a+25b) then prove 7|(10a+11b)

A: 7 | (17a+25b)  => There exist some integer k such that       17a+25b = 7k

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Q: 1a.) 0x**3  + 9x**3  1b.) 4X**3  - 9x**5  1c.) (3x   + 1x**3) + 2(9x**3 +(-3x)) 1d.)…

A: 1a.) 0x**3  + 9x**3 1b.) 4X**3  - 9x**5 1c.) (3x   + 1x**3) + 2(9x**3 +(-3x))1d.)…

Q: Solve the following differential equations indicating its characteristic equation, calculating the…

A: Solve the following differential equations indicating its characteristic equation, calculating the…

Q: Suppose L = {+, x, S, <, 0} is the first-order language of number theory (Peano's arithmetic). Write…

A: Given that L=+,×,S,&lt;,0 is the first order language of number theory (Peano's arithmetic). Now we…

Q: If n is an odd integer, then the floor of n/2 = (n-1)/2.

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Q: (a) Let the integers 1 to 23 be written on a straight line. Can you insert “+” and “−“ signs between…

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Q: For each integer n>1, let A(n) denote the sum of the integers from 1 to n. For example,…

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Q: Which of the following would represent an odd number? (A) 2x (B) 3x (C) 2x +2 (D) 2x + 1 O A В…

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Q: Let -6 M = Find formulas for the entries of M", where n is a positive integer.

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