Theorem 1 (Limit Comparison Test). Let an and bn be sequences such that an ≥ 0 and bn > 0 for all n € N. If lim (%) = = c with c a positive real number, then either Ean and Ebn both converge or both diverge.

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that  if x=4,8,3,-2

Q: Sum of seriy n=1 2"+1 4ª

A: Explanation of the answer is as follows

Q: + -3 -2 4 3 2 -2 2 (3.8, 0) 3 4 5 LO

A: 1. Center (0,0)Vertices  (0,1) and (0,−1)Foci  (0,5386​​)and(0,−5386​​)            or…

Q: 8 X - 3 = 5 + 4 X

A: We have8X-3 = 5 + 4XOn subtracting 5 and 4X on both side, we get8x- 3 -5 -4X = 04X - 8 = 0

Q: 7 X= |x - 3 10 18

A:

Q: 27. (xa is an odd number between and 9, inclusive}

A:

Q: Queslion lo

A:

Q: 30<2x+6<48

A: Given,           30<2x+6<48

Q: VXER, 3 yER, x-y =

A: Given that : The statement : ∀ x ∈ℝ , ∃ y ∈ℝ , x - y = 5. The statement is false.

Q: Evaluate doc 2³ +€ te

A:

Q: -4-3|4-4*2|

A: This is a basic question including a modulus function. in this |4-4*2|=|4-8|=|-4| Modulus function…

Q: Simplify the following expression: x5 + x3 =

A: The given expression is x-5÷x-3 As we know  x-n=1xn

Q: 3-3+1=?

A: NOTE As you don't mention what to find. I am just simplify the expression.

Q: +1 27+1 1

A: For the solution of the problem follow the next steps.

Q: 6 -81 3 II

A: We have to find the value

Q: show/prove what the answer is to 0 divided by 4 is

A: show/prove what the answer is to 0 divided by 4 is.

Q: (9, -7) (3, 1). Find 吕 ロ师仁 ?

A:

Q: 1+2+3+......+100

A: Concept Used: Arithmetic Progression : If S=1+2+3+.......+n then first term of the sum is 1 and last…

Q: + - ..+(-1)28 . ) 28_728 15

A: The given series sum is 1-71+491-…+-128728128. The first term of the above series is 1 which can be…

Q: Evaluate I = | 5+ 3r3 dr

A:

Q: 1 + 3 + 5 + 7 all the way to 99

A:

Q: 2+2? how

A: Given query is to find the value of the expression.

Q: ८ 2x-7 9 CE

A: Thank you 😊