n²-7n +3 | + 10n-4n2 n2 4 + n3 In (n+2) in(1+4n)

Q: 18) 5-D*n 5n+2 (-1)".n

A: Given∑n=1∞(-1)n.n(5n+2)Now we apply the series divergence testaccording to series divergence testif…

Q: n 2n + 2 /2 n 2n k k=1 \k –1, п+1 n -

A: The objective is to prove that ∑k=1nnknk-1=2n+2n+1/2-2nn This theorem can be proved by induction,…

Q: 2 4 8 n2 + 2n 1 (i) 1 3 (ii) (iii) ) - 9 27 1+ 2n2 ' n=0 2nn n=1

A: Both series we can evaluate using geometric series method.

Q: n2 -5n +4 an 3n2 +5 n-1 Vn=6n- 3 4 %D Wn = 4 %D -/3 II

A:

Q: 3Fn - F n-2= Fn+2 for n>3

A:

Q: ( a ) Ση-1 (b) En=2 n7-1 15n-2 (c) En=1 11n+3 1 (d) Σn1 n14 (-1)" (e) En=1 7n+4

A:

Q: n2 – n 1 2n² + n الم نابعة زختبر تقارب -

A:

Q: e3t -1-3t { 9 O 3/(s^2(s-3)) O 1/(s^2(s+3)) O -3/(s^2(s+3)) 1/(s^2(s-3))

A:

Q: 2 2 n(n-1)x", n²-n 37

A:

Q: { :Find the first 3 terms for 2n-1 (2n-1)! (−1)n+¹

A: given sequence  -1n+1x2n-12n-1!

Q: 2n2 + n8 1. 935n10 + 7n² + 6 9n5 + n² – 9n 2. 7n13 6n10 + 5 бп? + 9n7 3. 2n8 + 7n³ – 2 n=1

A:

Q: a) 5n + 1 3n2 2" (b) Σ 1 ( c) Σ n=2 nº - 7 - 1 n=1 n=1 3n

A:

Q: -2n2n 2n n 2) п En=1 1 —

A: Given series is ∑n=1∞1-2n2nn2n

Q: b) 13 + 33 + 53 + .. + (2n – 1)³ = n²(2n² – 1) - Ensure that you explain the steps taken.

A: Explanation is given as follows:

Q: Identify the two series that are the same.

A: In order identify the same series, just write the few terms of the gives series as follows. (a)…

Q: (-1)n+13n (b) n5n n=1

A:

Q: 3. 1+-=. 1. х*— 13х2 + 36 %3D 0 2. ха — хе -2%3D 0 3 3. 2n 2 n2

A:

Q: Solve for n. k (3-n) %3D

A: b=k(3-n)pbp=k(3-n)

Q: 1 Σ (-3)²+" (n² + 1) -(4x – 12)" n n=0

A:

Q: 2 4 + 27 (-2)" 16 + 243 Σ %3D - 3n+k n=1 9. 81 what must be the value of k?

A:

Q: 5) h(n) =-2n² + 4; Find h(4)

A:

Q: n 4n – 1

A:

Q: (2n + 1)(n² + 1) (e) > (n – 1)(n² – 4)² | n=3

A: The given series is divergent.

Q: 4n +1 (a) 2n2 +3 n=0 5n2 – n+1

A: Since multiple questions are asked, I am answering first question

Q: n(n + 1)(2n + 1) 6 k=0

A: In this question, we prove the sum of squares of natural numbers.

Q: 2(n!)2 (2n)! n=1

A:

Q: 2n+2 – 3" Σ - 2. Determine 6n+1 n=0

A: To find: ∑n=0∞2n+2-3n6n+1

Q: 4n + 7 Σ (i) (ї) Z(n² – 8n + 16) 5n n=1 n=5 8

A:

Q: 8. x- 3x + 2 = -8 9. 7z -3 = 3 +6z 10.-8 -n = n- 4n 11.4n – 40 = 7(-2n + 2)

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Q: 2" (a) 3 3n+1 (c) E(-1)"; 4n n=1 (b) 3+5n² (4) E n+ n2 n=1 n=1

A:

Q: 3.6...(3n) E=1(-1)" n=1 2n2.5...(3n-1)

A:

Q: n Σ k + 2n + n2 | n k=1

A: use the sum of first natural number  to evaluate the sum

Q: -n 2n+5

A: We have given a series.

Q: e) Un n²-3n+ 1 2n²+1

A: Introduction: A sequence is a collection of functions. This function makes a map from the set of…

Q: true or false. 3Fn > Fn+3 for n = 3

A: Answer is True

Q: 8. Ση-0 ne-1 4n 9. En=0 (n+2)3 n=0 (n+2)³ 3. 10. Σ0 n-3n+2 %30 n2-3n+2

A:

Q: 6 - 22n-1 5n+1 n=1 =D1

A: Given: ∑n=1∞6×22n-15n+1 A ∑n=1∞fn series is convergent if, fn+1fn<1 Check the convergence of the…

Q: n+1 2n + 1 5+8n² (b) t = 2-7n² (c) t₁ = (-1)" (1₂2) n+2) (a) t₁ =

A:

Q: Σ 2n+3 + n2 +3n n-1 3.

A: Given series ∑n=1∞1n2+3n+2n+33n

Q: S (2n)!n² (2n + 2)!

A: We have to find  limn→∞(2n)! n2(2n+2)!

Q: Σ 2n (2n - 1)2(2n + 1)2 n=1

A: The given series is: ∑n=1∞2n2n-122n+12 By the result of Comparison test, if ∑un and ∑vn are two…

Q: (-1)".n -1)".n 5n+2

A:

Q: 2n ( a ) Ση (v 1 (b) -1)^2?n+13 2n + 1 5n n=1 n=0

A:

Q: 13) b - 6b + 8 14) n + 6n + 8 15) 2n + 6n - 108 16) Sn' + 10n + 20

A:

Q: 7 7n2 –n – 2 > 4n2 4n 4 — Зп + 1

A: We have to prove that 7n2-n-24n4-3n+1<74n2. For this, we will consider the terms 7n2-n-2 and…

Q: 2) . (4а — 2)2n+1 n! n=0

A: Given series is ∑n=0∞4x-22n+1n!

Q: 2 -3 +21 -1 0 2 Find A in AT+ -1-3

A: Given:AT+52-1-3-1=2-3-10+2I Let the matrix A be,A=abcdAT=acbd So,…

Q: n° n=1 3n2 en Σ: 22n 2 2n + 1 n=1

A: Since you have posted multiple question in this question which are not interlinked so i have solved…