Determine the limit of the sequence $a _ { n } = [ \ln ( n + 1 ) - \ln ( n ) ]$ .
A) $\frac { 1 } { e }$
B)1
C)2
D)0
E) $e$
F) $\frac { 1 } { 4 }$
G) $\ln 2$
H)Divergent

Question

Determine the limit of the sequence $a _ { n } = [ \ln ( n + 1 ) - \ln ( n ) ]$ .
A) $\frac { 1 } { e }$ 
B)1
C)2
D)0
E) $e$ 
F) $\frac { 1 } { 4 }$ 
G) $\ln 2$ 
H)Divergent

Quizplus · Accepted Answer

The limit of the sequence $a_n = \ln(n + 1) - \ln(n)$ can be simplified using the properties of logarithms to $\ln\left(\frac{n + 1}{n}\right)$. As $n$ approaches infinity, the fraction $\frac{n + 1}{n}$ approaches 1, and the natural logarithm of 1 is 0. Therefore, the limit of the sequence is 0.

Determine the Limit of the Sequence an=[ln⁡(n+1)−ln⁡(n)]a _ { n } = [ \ln ( n + 1 ) - \ln ( n ) ]an​=[ln(n+1)−ln(n)]

Determine the Limit of the Sequence $a _ { n } = [ \ln ( n + 1 ) - \ln ( n ) ]$