2. Determine if each sequenceconverges or diverges. If it converges find the limit. Clearly explain your reasoning **Mathematical Sequences****g) Given Sequence:**\[ a_n = \ln(n + 1) - \ln(n) \]This sequence represents the difference between the natural logarithms of consecutive integers. The natural logarithm function, denoted by \(\ln\), is the inverse of the exponential function \(e^x\). This expression can also be rewritten using logarithmic properties as:\[ a_n = \ln\left(\frac{n+1}{n}\right) \]**h) Given Sequence:**\[ a_n = \frac{(-3)^n}{n!} \]This sequence involves the exponential term \((-3)^n\), where n is the term position, divided by the factorial of n, denoted by \(n!\). The factorial function \(n!\) is the product of all positive integers up to n. This expression describes a sequence that involves both exponential growth and factorial growth, which is useful in understanding series expansions like the Taylor series.

Name: 2. Determine if each sequenceconverges or diverges. If it converges fi
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: 2. Determine if each sequenceconverges or diverges. If it converges find the limit. Clearly explain your reasoning **Mathematical Sequences****g) Given Sequence:**\[ a_n = \ln(n + 1) - \ln(n) \]This sequence represents the difference between the natu