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 involves a product in the numerator that grows with each term, but the denominator grows as the square of $n$, which means it grows faster than the numerator. As $n$ approaches infinity, the fraction's value approaches 0 because the denominator's growth rate outpaces the numerator's growth rate.

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 $\left\{ \frac { 1 \cdot 9 \cdot 17 \cdots ( 7 n + 1 ) } { ( 7 n ) ^ { 2 } } \right\}$