Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$a + a r + a r ^ { 2 } + \ldots + a r ^ { 10 }$
A) $\sum _ { i = 1 } ^ { 10 } a r ^ { i }$
B) $\sum _ { \mathrm { i } = 1 } ^ { 10 } \left( \mathrm { ar } ^ { \mathrm { i } } - 1 \right.$
C) $\sum _ { i = 1 } ^ { 11 } a r ^ { i - 1 }$
D) $\sum _ { i = 1 } ^ { 10 } ( a r ) ^ { i }$

Question

Quizplus · Accepted Answer

The given series is a geometric series starting from $a$ (which can be written as $a r^0$) and ending at $a r^{10}$. To express this using summation notation starting from 1, we adjust the exponent to $i-1$, so the correct notation is $\sum _ { i = 1 } ^ { 11 } a r ^ { i - 1 }$, which matches option C. This notation correctly represents the series from the first term $a$ (when $i=1$, the exponent is $0$) to the last term $a r^{10}$ (when $i=11$, the exponent is $10$).

Express the Sum Using Summation Notation a+ar+ar2+…+ar10a + a r + a r ^ { 2 } + \ldots + a r ^ { 10 }a+ar+ar2+…+ar10

Express the Sum Using Summation Notation $a + a r + a r ^ { 2 } + \ldots + a r ^ { 10 }$