MAT2613 Assignment 2 solutions 2026
UNISA
Closing Date: 28 AUGUST 2026
Total Marks: 50
UNIQUE ASSIGNMENT NUMBER: 197336
All questions solved with full working. If need assignment or exam help any module
reach me 0793226427
MAT2613 Assignment 02 Complete Solutions
, Question 1
Determine using the Ratio Test whether each series converges or diverges.
1.1
∞
3𝑛
∑
𝑛!
𝑛=1
3𝑛
Let 𝑎𝑛 = 𝑛!
Ratio Test:
𝑎𝑛+1
𝐿 = lim ∣ ∣
𝑛→∞ 𝑎𝑛
Substitute:
3𝑛+1
𝑎𝑛+1 =
(𝑛 + 1)!
Then
𝑎𝑛+1 3𝑛+1 𝑛!
= ⋅ 𝑛
𝑎𝑛 (𝑛 + 1)! 3
Simplify:
3 ⋅ 3𝑛 𝑛!
= ⋅ 𝑛
(𝑛 + 1)𝑛! 3
3
=
𝑛+1
Take limit:
3
𝐿 = lim
𝑛→∞ 𝑛 + 1
𝐿=0
Conclusion
Since 0 < 1
UNISA
Closing Date: 28 AUGUST 2026
Total Marks: 50
UNIQUE ASSIGNMENT NUMBER: 197336
All questions solved with full working. If need assignment or exam help any module
reach me 0793226427
MAT2613 Assignment 02 Complete Solutions
, Question 1
Determine using the Ratio Test whether each series converges or diverges.
1.1
∞
3𝑛
∑
𝑛!
𝑛=1
3𝑛
Let 𝑎𝑛 = 𝑛!
Ratio Test:
𝑎𝑛+1
𝐿 = lim ∣ ∣
𝑛→∞ 𝑎𝑛
Substitute:
3𝑛+1
𝑎𝑛+1 =
(𝑛 + 1)!
Then
𝑎𝑛+1 3𝑛+1 𝑛!
= ⋅ 𝑛
𝑎𝑛 (𝑛 + 1)! 3
Simplify:
3 ⋅ 3𝑛 𝑛!
= ⋅ 𝑛
(𝑛 + 1)𝑛! 3
3
=
𝑛+1
Take limit:
3
𝐿 = lim
𝑛→∞ 𝑛 + 1
𝐿=0
Conclusion
Since 0 < 1
