an = 0 and bn Σ-1 bp Show that if lim n converges then En-1an converges too.

Q: If 2a, converges, then 1. diverges Select one: True False

A: Use the defination of convergence of a series.

Q: Show that the series Ln=l 12+2z10n-5z"ª –3z+2;10n converges absolutely for |리 < 1.

A: The series ∑n=1∞an is absolutely convergent if the series ∑n=1∞an  Ratio test:  The series ∑n=1∞an…

Q: If lim an 1 then n00 Σ an n=1 converges O diverges O may or may not converge

A:

Q: 3 converges conditionally because lim n - 3 = 0. 3n + 1 3n + 1 True False

A: The given question is solved with explanation below.

Q: 1 converges conditionally because lim 第-1 = 0. 2n n=1 True False Reset Selection

A: this is false becuse

Q: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

Q: Determine whether the given converges or diverges. n Σ 2n + 1 n=1

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

Q: Determine whether the following converges or diverges {(5) n 2n +1 n=1

A:

Q: The series Σ 6( − 1)*0.2-1.9/k○ diverges converges. k=0

A: We use ratio test to find the desired result.

Q: 1 Determine whether (-1)". converges conditionally, absolutely, or not at all. Vn2 + 1 n=0

A:

Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

A:

Q: Suppose {fn}=1 and {g„}=1 converges uniformly on E where {fn}=1 and {gn}n=1 are sequences of bounded…

A: Let fnn=1∞ is converges uniformly to f and gnn=1∞ is converges uniformly to g on E and fnn=1∞ and…

Q: The series > (2)k-1 converges. k=1 Select one: True O False

A:

Q: 7N 8N 3) Show that converges/diverges.

A:

Q: The following series Σ 3n-2" 5n+1 n=0 is convergent to

A: this is convergent series and

Q: Determine whether En=1n converges or m%3D1 2n

A: Given: ∑n=1∞n2n

Q: The series 7 2n E,(-1)" 4 n= is absolutely convergent. Select one: True O False

A: Root Test : Suppose we have series ∑ an .Define,                          L = limn→∞ an1n .Then ,(…

Q: Show that E-2 ((In n)ª/n²) converges for -o 1. n=2

A:

Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: (3n)" (2n + 50)" n=1

A:

Q: If lim a, is not 0 then 2 a, is convergent n=1

A: By using theorem we can say that

Q: (- 1)"+(- =D1 converges conditionally in elect one: True

A: Please refer to the image below

Q: If 2, =1ª, converges conditionally then E=|92| diverges 'n=D: Select one: True False

A:

Q: 1 3. En=1 (2n+1)3

A:

Q: Determine whether the given converges or diverges. n 2n +1 n=1

A: We can solve this as follows:

Q: If an < bn and if En=1 an converges, then 1 bn also converges. True False

A: we can solve it by using comparison test.

Q: 2 n 1 o Show that + converges/diverges n-

A:

Q: The series k=1 5( − 1)k+1 - kl.1 O converges diverges.

A:

Q: Show that if $a_{n}&gt;0$ and $\Sigma a_{n}$ is convergent, then $\Sigma \ln \left(1+a_{n}\right)$…

A: Here, we are given that an &gt; 0 and series is convergent. We need to prove that: is convergent.…

Q: If {fn}n=1 is a pointwise convergent, then {fn}=1 is uniformly convergent.

A:

Q: N 2N + 1 2) Show that converges/diverges. +

A: We have to show whether the series converges or diverges.

Q: If E an converges, then an/n12 converges. n=1 n=1 O True False

A: True, using Abel's test.

Q: .8.8 Suppose that Cn >0 for each n E N. Prove that n either converges = diverges to infinity.

A:

Q: (-1)" In(n) Vn n=2

A:

Q: - 1)n+'] (a) Converges to Diverges .......... 5"

A:

Q: ,(-1)" converges conditionally, but not absolutely. Show all work. 3n Prove E

A:

Q: 1 x converges 1 ex - e-X Select one: True False

A:

Q: Given that " In (1) converges, does [.. converge or diverge? In(n) 1 (²+5)² A. Diverges B. Cannot be…

A: Let ∑pn and ∑qn are two series such that pn≤qn. If ∑qn is convergent, then ∑pn is convergent.

Q: Consider the sequence S n²r(1 – nx) x € [0, 1/n] - fn(x) := 0. elsewhere . Show it converges…

A: Let gx=n2x1-nx Differentiating wrt x, we get  g'x=n2-2n3x Putting g'x=0, we get  n2-2n3x=0⇒x=12n

Q: Suppose {fn}n=1 converges uniformly on E. Show {fn}n=1 converges pointwise on E.

A:

Q: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

A:

Q: 1dx x²+2x+5 -00 O diverges O None 37 converges to 4 converges to converges to converges to 3r

A:

Q: 5) Find all values of x for which En=1 nxn (n+1)(2x+1)n converges absolutely.

A:

Q: Find the values of p such that E(-1)"- converges.

A: The given series :

Q: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

A:

Q: п — 1 п — 1 2( 1)" " converges conditionally because lim 2" 0. 27 n00 n=1

A:

Q: Determine if the given is convergent or divergent. E0, In" (n*) 23n2 n=1

A:

Q: (-1y" In n 1) Determine if £∞ n=1 Absolutely converges, converges conditionally, or diverges.

A:

Q: 6n2 n

A: The given sequence be 6n2en To find it is convergent or divergent

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.