Find the value of the limit for the sequence given. $\left\{ \frac { 1 \cdot 9 \cdot 17 \cdots ( 7 n + 1 ) } { ( 7 n ) ^ { 2 } } \right\}$
A) $0$
B) $- 1$
C) $\pi$
D) $3$
E) $1$

Question

Quizplus · Accepted Answer

The sequence is a product of terms in an arithmetic sequence divided by a power of $7n$. As $n$ approaches infinity, the numerator grows slower than the denominator, leading the limit to be $0$.

Find the Value of the Limit for the Sequence Given {1⋅9⋅17⋯(7n+1)(7n)2}\left\{ \frac { 1 \cdot 9 \cdot 17 \cdots ( 7 n + 1 ) } { ( 7 n ) ^ { 2 } } \right\}{(7n)21⋅9⋅17⋯(7n+1)​}

Find the Value of the Limit for the Sequence Given $\left\{ \frac { 1 \cdot 9 \cdot 17 \cdots ( 7 n + 1 ) } { ( 7 n ) ^ { 2 } } \right\}$