Write the series in summation notation. $$z ^ { 5 } + z ^ { 10 } + z ^ { 15 } + z ^ { 20 } + z ^ { 25 }$$
A) $\sum _ { j = 1 } ^ { 5 } z ^ { 5 j }$
B) $\sum _ { j = 5 } ^ { 25 } z ^ { j }$
C) $\sum _ { j = 5 } ^ { 9 } z ^ { j }$
D) $\sum _ { j = 1 } ^ { 25 } z ^ { 5 j }$

Question

Quizplus · Accepted Answer

The series increments by powers of 5, starting from $z^5$ to $z^{25}$, which matches the pattern of $\sum _ { j = 1 } ^ { 5 } z ^ { 5 j }$, where $j$ starts at 1 and goes to 5, each time multiplying $j$ by 5 to get the exponent of $z$.

Write the Series in Summation Notation z5+z10+z15+z20+z25z ^ { 5 } + z ^ { 10 } + z ^ { 15 } + z ^ { 20 } + z ^ { 25 }z5+z10+z15+z20+z25

Write the Series in Summation Notation $z ^ { 5 } + z ^ { 10 } + z ^ { 15 } + z ^ { 20 } + z ^ { 25 }$