Use the Geometric Sum identity to prove that, if r 70, then (1 – x)3 1 =1+ (1 - x) + (1 – x)² + |

Q: 3x° + x-10 37x+38 a) Show that 3x-12 + x2 + 4x+4 (x+2)

A: To show that, 3x3+x-10x2+4x+4=3x-12+37x+38x+22

Q: (a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c)…

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Q: The sum + is between 8 (A) and 3 (B) and 1 (C) 1 and 1 14/ D) 1 and 1/2 E) 1 and 2

A: The given is  Sum of this can be calculated  as           =                         =…

Q: 4x 4 lim,-1* - x-1 In x 4 3 5 1 O 2

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Q: Show that if x > 0 and |x² – 9| < 2, then |x - 3| < 1.

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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: Show by contraposition that : Vx ERX2-3x - 1020 → x25 or x< - 2

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Q: (c) Prove that r| +11 36 T-1 2 +36 for all real I.

A: We have to prove that the following inequality holds: x-11x2+36≤x+1136 for all real x. We will use…

Q: Find the adjoint of the operation B = 2|0 × 1|- ; | 1 ×o |

A: This question asks to find the adjoint of the operation B^=2|0×1|-i|1×0|.

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: fnd all xeR where -5x (x+) n=2 ナS is Convergent- +5

A: We have to find all x∈ℝ such that the series ∑n=2∞ -5xx+1nx+1n-1+5x+1n+5 is convergent. We know that…

Q: Prove that for all positive real a we have 22 +5 20x4 2 4/5. 24 x2 +5

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Q: 5x+h over 5x+h+3 minus 5x over 5x+3, all over h. This is a difference quotient problem in…

A: LCD of the numerator is (5x+5h+3)(5x+3).We make both denominators same then subtract the rational…

Q: given 7(x-1)=2(3x+2) prove x=11

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Q: Evaluate x +3 dx (x – 1)(x² + 25)

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Q: Find the Domain of 1, if f(=) 0(s-6) %3D O Domain: y is all real numbers O Domain: y N0 O Domain: NO…

A: Given f(x)=6(x-6)2 To find f-1, assume y=f(x) then swap variables to find f-1

Q: Prove that product notation d/n = nτ(n)/2.

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Q: (b) Given integers a, b and c such that cla and cb then c|(ar + bs) for all r, s E Z. True False &…

A: Given that c|a and c|b for some given integers a,b and c The statement is c|ar+bs for all r,s∈ℤ…

Q: Prove that if |x-1| < 1, then x² - 2x + 5| < 8.

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Q: 1 f X~ N(0,0²), then X² ~G (¹2¹2) Prove this statement

A: Given  X~N(0, σ2)

Q: Vx x² >0

A: Integer, whole-valued positive or negative number or 0. The integers are generated from the set of…

Q: (c) Prove that x - 11 |x| + 11 |x² + 36| 36 for all real r.

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Q: Show that * y = (y² – r*)(2² – x*)(2² – y³)

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Q: Suppose SCR is a set of numbers. (a) Define inf(S) and sup(S). (b) Show that inf(S) = - sup(-S). (c)…

A: Set: A well-defined collection of objects or numbers is called a set. We can write a set in two…

Q: Let x = 2 and y=3. Compute 7 ||x - y||₁ = ||x - y||∞o = ||x - y||₂=

A: Given :- x=-527,y=231

Q: For an integer t, prove that gcd(2t + 1, 9t + 4) = 1.

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Q: Prove that the expression 2y2 - 128 is equal to 2(x2+2) (x² – 2) (x³ + 4x* + 16).

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Q: inc

A: Our Aim is to find the consecutive integers such that  the sum of their squares is 202.

Q: Simplify the expression Y = bar((AB + bar C) (bar (A + B) + C)) Obtain the canonical product of sum…

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Q: Find the term of (a – 2b)3 that has b in it. |

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Q: 2. [(x – 1) + 5][(x – 1) – 51]. Write the answer in the standard form

A: To write in standard form.

Q: For -3-3: (a) Find the modulus and argument of z. (b) Express + in the form of a+ib where a,beR.

A: This is a problem related to complex number. Based on the general concept and formula used for…

Q: x² + 6x – 1

A: We have to express  x2+6x-1 in the form (x-m)2+n.

Q: 2+ 3x (7x – 1)²(x – 8)

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.