Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
-$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 15 }$$
A) $\sum _ { \mathrm { k } = 1 } ^ { 15 } a r ^ { \mathrm { k } }$
B) $\sum _ { k = 0 } ^ { 15 } a r ^ { k }$
C) $\sum _ { \mathrm { k } = 1 } ^ { 16 } a \mathrm { r } ^ { \mathrm { k } }$
D) $\sum _ { k = 0 } ^ { 15 } ( a r ) ^ { k }$

Question

Quizplus · Accepted Answer

The given series is a geometric series starting from $a$ (which can be written as $ar^0$) and ending at $ar^{15}$. The correct summation notation starts with $k=0$ to include the first term $a$ as $ar^0$ and goes up to $k=15$ to include the last term $ar^{15}$.

Express the Sum Using Summation Notation a+ar+ar2+…+ar15a + a r + a r ^ { 2 } + \ldots + a r ^ { 15 }a+ar+ar2+…+ar15

Express the Sum Using Summation Notation $a + a r + a r ^ { 2 } + \ldots + a r ^ { 15 }$