whether given sequences are convergent or divergent. Show your work. 4n2 +1 In 3n (b) ат — In 5n Vn³ – Vn? 12n2 (с) а, — (а) ап — Зп + 2 n + 2

Q: Determine if the following sequences are arithmetic or geometric, if they have a common difference…

A: Q2)Given,-6,-2,2,6,10,14,...we can see that:-6 + 4 = -2-2 + 4= 22+4=66+4=1010+4=14So, it is in…

Q: 2) Evaluate the following finite sum in terms of N: (1+k+ k²) k=1

A: Given: ∑k=1N(1+k+k2)

Q: Simplify by combining the two sums and find an erplicit formula. That is, your answer should not…

A: Simplify by combining the two sums and find an explicit formula. That is, your answer should not…

Q: Suppose you have a sequence {W1,W2,W3,W4, . . . } given recursively by Wn = 4Wn−1 − Wn−2 − 6Wn−3,…

A:

Q: (3) Find all p ER so that 3n² + 2n +1 n2p-1 + 137 n=1 converges. As always, your answer must be…

A:

Q: Use power series methods to solve the DEs below about x0. You may leave your answer in terms of a…

A:

Q: (a) (b) Find the limit of the following sequences or show why they diverge. In(5n6) 1 7n-1 +n8 8n³ +…

A:

Q: 30 (a) Find the sum of 2k+1. k=2 (b) Show that if Re z < 0, then Je| <1 and find the sum of ) ek*.…

A: i have given the formulas that i have used in the step where i have used them

Q: g(a) gla) - 9(a) 2 a - 8 a +8 For the case g(a) < 0, consider the function -g. consequence of this…

A:

Q: B: 20. Find a recursive formula for the Fa₁ = G a 1 = 18, an = −6an - 1, n ≥ 2 18, anan-1 - 6, n ≥ 2…

A: Step 1: Step 2: Step 3: Step 4:

Q: (3) Σ Σ Σ (2 + j) = tw4f=2k=1 6 7 2

A: As all the questions are different and independent to each other, we shall solve first question only…

Q: 04 * 1 2 3 Suppose that three sequences, {an}_1 {bn}a_1 and {n}a_₁ are defined by 17n²+10n+7 117n²+3…

A:

Q: 04 * O O C O 0 1 2 3 Suppose that three sequences, {an}, {bn}_1 and {n}a_₁ are defined by 17n²+10n+7…

A:

Q: 1+ 2n² Xn {Tn} 1– 3n2 - Prove that the sequence where is bounded.

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.