Write the sum using sigma notation. Begin with $k = 0$ . $\frac { 1 } { 9 ^ { 0 } } - \frac { 1 } { 9 ^ { 1 } } + \frac { 1 } { 9 ^ { 2 } } - \frac { 1 } { 9 ^ { 3 } } + \ldots - \frac { 1 } { 9 ^ { 11 } }$
A) $\sum _ { k = 0 } ^ { 10 } - \frac { 1 } { 9 ^ { k } }$
B) $\sum _ { k = 0 } ^ { 11 } \left( - \frac { 1 } { 9 } \right) ^ { k + 1 }$
C) $\sum _ { k = 0 } ^ { 10 } \left( - \frac { 1 } { 9 } \right) ^ { k + 1 }$
D) $\sum _ { k = 0 } ^ { 11 } - \frac { 1 } { 9 ^ { k } }$
E) $\sum _ { k = 0 } ^ { 11 } \left( - \frac { 1 } { 9 } \right) ^ { k }$

Question

Quizplus · Accepted Answer

The series alternates signs and starts with a positive term, which can be represented by $(-1)^k$. Since the first term corresponds to $k=0$ and is positive, the series can be written as $\sum _ { k = 0 } ^ { 11 } \left( - \frac { 1 } { 9 } \right) ^ { k }$, where the exponent $k$ directly applies to the entire fraction, correctly alternating the sign for each term in the series.

Write the Sum Using Sigma Notation k=0k = 0k=0 190−191+192−193+…−1911\frac { 1 } { 9 ^ { 0 } } - \frac { 1 } { 9 ^ { 1 } } + \frac { 1 } { 9 ^ { 2 } } - \frac { 1 } { 9 ^ { 3 } } + \ldots - \frac { 1 } { 9 ^ { 11 } }901​−911​+921​−931​+…−9111​

Write the Sum Using Sigma Notation $k = 0$ $\frac { 1 } { 9 ^ { 0 } } - \frac { 1 } { 9 ^ { 1 } } + \frac { 1 } { 9 ^ { 2 } } - \frac { 1 } { 9 ^ { 3 } } + \ldots - \frac { 1 } { 9 ^ { 11 } }$