11. a) Find a formula for 1 +... + 2" by examining the values of this expression for small values of n. b) Prove the formula you conjectured in part (a).

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Q: 11. Is there a formula for this sort of question?

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Q: 13 e, thank you.

A: e)Given that, sum of the first n terms of the given series is

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

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Q: nen 1/2 is a positive odd integer. ed

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Q: Let A = (-n/(n + 2) : n E N}. (a) Give the e-s definition of the infimum. (b) Using item (a), show…

A: Given; A=-n/(n+2).

Q: 1 := 0 +1 n=0

A: The following proof has been done in step 2.

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Q: · Find (with proof) the residue of 320222022 when dividing it by 31.

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Q: (a) Prove, by mathematical induction, that for every positive integer n, 7² r² = (n + 1)² T=1

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Q: 16. How many terms are needed to approximate 2(-1)"+1 (÷) with an error of less than 0.001?

A: The given alternating series is: ∑n=1∞(-1)n1n4 Let, an=1n4

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Q: gcd(a,b) = (a+b, lcm(a,b))

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Q: 5 find the quotient i15-as a" by long division meth od 1-a

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Q: Part III: Prove the following 5. Prove that 32.753215321... is a rational number.

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Q: What is the most appropriate translation of the given mathematical symbols below? * να R, α > 0,…

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Q: An algebraic attempt to solve the expression n-1Cn-3 = 21 is shown below. (n - 1)! = 21 2!(n – 3)!…

A: We have to find the error

Q: 4. Solve the following. (a) Show that 3 is a primitive root of 343.

A: A number g is called a primitive root modulo n if every number co prime to n is congruent to a power…

Q: 2. Show that x - 5x² - 7 = 0 can be arranged to give the formula: x n+1 = √√5(x3) + 7 Using a value…

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Q: Show between any two irrational numbers there is an irrational number. (Hint: Assume r and s are…

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Q: (2) Prove that (1+x)" > 1+nx for all x > 0 and n > 1.

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Q: 5.( Use the methods of this class to find two numbers, x and y, whose sum is 10 and with the…

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Q: 37! D- Given that N= (191)(15) is an integer: i- Does the prime 11 divide N? What about the prime…

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Q: Prove: An odd plus an odd equals an even. (2m + 1) + (2n + 1) = [ ? ]m +[ ]n+ [ ] = 2(m + n + [ ) =…

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Q: 2. 3. By "Pythagorean triple" (a, b, c), Pythagoras and the Babylonians gave a formula for…

A: Proof:It is enough to show that (2m, m2 – 1, m2 + 1) satisfies a2 + b2 = c2.

Q: III. Prove the following using Indirect Proof. 10. If x3 is an even number, then x is an even…

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Q: Let m and n be positive integers. Show that mZ+nZ= (m, n)Z.

A: Given: Let m, n be two positive integers. To prove: mℤ+nℤ=m,nℤ. Proof: Let I=mℤ,J=mℤ Since…

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Q: 2.5 3.5 5.5 The approximation of which irrational number is shown by point R on the number line? O…

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Q: 6. (i) Sketch the proof of the existence of a positive number satisfying the equation a2 = 5. We…

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Q: ind two consecutive positive integers whose product is 240 use polya’s four-steps in problem-solving

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Q: How many multiplicity of - 1 are there in the roots of x +3x2 + 3x+1 0? O 1 O 2 3 O 4

A: Given equation  x3+3x2+3x+1=0

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Q: Find (with proof) the residue of 320222022 when dividing it by 31.

A: Given number is 320222022 Let the remainder(residue) be x when 320222022 divide by 31 x=32022202231…