Find the limit of the sequence $a _ { n } = 1 + \left( - \frac { 4 } { 5 } \right) ^ { n }$ .
A)0
B) $- \frac { 4 } { 5 }$
C) $\frac { 4 } { 5 }$
D) $- \frac { 1 } { 5 }$
E)1

F) $\frac { 1 } { 5 }$
G)-1
H)Divergent

Question

Find the limit of the sequence $a _ { n } = 1 + \left( - \frac { 4 } { 5 } \right) ^ { n }$ .
A)0
B) $- \frac { 4 } { 5 }$ 
C) $\frac { 4 } { 5 }$ 
D) $- \frac { 1 } { 5 }$ 
E)1

F) $\frac { 1 } { 5 }$ 
G)-1
H)Divergent

Quizplus · Accepted Answer

The sequence $a_n = 1 + \left(-\frac{4}{5}\right)^n$ approaches 1 as $n$ goes to infinity because $\left(-\frac{4}{5}\right)^n$ approaches 0 (since $-\frac{4}{5}$ is between -1 and 1, its powers get closer and closer to 0).

Find the Limit of the Sequence an=1+(−45)na _ { n } = 1 + \left( - \frac { 4 } { 5 } \right) ^ { n }an​=1+(−54​)n

Find the Limit of the Sequence $a _ { n } = 1 + \left( - \frac { 4 } { 5 } \right) ^ { n }$