Write the sum using sigma notation. Begin with $k = 1$ . $\frac { 1 } { 1 ^ { 3 } } + \frac { 1 } { 2 ^ { 3 } } + \frac { 1 } { 3 ^ { 3 } } + \frac { 1 } { 4 ^ { 3 } } + \ldots + \frac { 1 } { 16 ^ { 3 } }$
A) $\sum _ { k = 1 } ^ { 15 } \frac { 1 } { k ^ { 3 } }$
B) $\sum _ { k = 1 } ^ { 15 } \frac { 1 } { ( k - 1 ) ^ { 3 } }$
C) $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { ( k - 1 ) ^ { 3 } }$
D) $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { ( k + 1 ) ^ { 3 } }$
E) $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { k ^ { 3 } }$

Question

Quizplus · Accepted Answer

The given sum starts with $k =1$ and goes up to $k = 16$, so we need a sigma notation that covers that range. The only option that satisfies this is E, which gives us the sum from $k = 1$ to $k = 16$ of $\frac{1}{k^3}$.

Write the Sum Using Sigma Notation k=1k = 1k=1 113+123+133+143+…+1163\frac { 1 } { 1 ^ { 3 } } + \frac { 1 } { 2 ^ { 3 } } + \frac { 1 } { 3 ^ { 3 } } + \frac { 1 } { 4 ^ { 3 } } + \ldots + \frac { 1 } { 16 ^ { 3 } }131​+231​+331​+431​+…+1631​

Write the Sum Using Sigma Notation $k = 1$ $\frac { 1 } { 1 ^ { 3 } } + \frac { 1 } { 2 ^ { 3 } } + \frac { 1 } { 3 ^ { 3 } } + \frac { 1 } { 4 ^ { 3 } } + \ldots + \frac { 1 } { 16 ^ { 3 } }$