Which of the Following Series Diverges?
1) $\sum _ { n = 1 } ^ { \infty } \frac { n + 2 } { n ^ { 2 } + 1 }$

question 308

Multiple Choice

Which of the following series diverges?
1) $\sum _ { n = 1 } ^ { \infty } \frac { n + 2 } { n ^ { 2 } + 1 }$ 2) $\sum _ { n = 1 } ^ { \infty } \frac { n ! } { 2 ^ { n } }$ 3) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 n - 1 } { n + 3 } \right) ^ { n }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

---

Definitions:

Short-term Profit

Profits earned over a short period of time, typically a quarter or a year, reflecting the immediate financial health of a company.

Long-term Profits

Profits generated over an extended period, indicating the sustainability and viability of a company's business model.

SVA

Stands for Shareholder Value Added, which is a measure used to evaluate a company's ability to generate wealth for its shareholders beyond the required rate of return on their investment.

PV of Cash Flows

The present value of expected future cash flows discounted at the relevant rate, reflecting the current worth of those cash flows.