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What is this series witten in sigma notation?

2.5+2.5(1.2)+2.5(1.2)^(2)+dots+2.5(1.2)^(87)
A.
sum_(i=1)^(87)2.5(1.2)^(k)
B.
sum_(i=1)^(8pi)2.5(1.2)^(k-1)
C.
sum_(i=1)^(88)2.5(1.2)^(k)
D.
sum_(i=1)^(88)2.5(1.2)^(k-1)

What is this series witten in sigma notation? $\newline$ $2.5+2.5(1.2)+2.5(1.2)^{2}+\ldots+2.5(1.2)^{87}$ $\newline$ A. $\sum_{i=1}^{87} 2.5(1.2)^{k}$ $\newline$ B. $\sum_{i=1}^{8 \pi} 2.5(1.2)^{k-1}$ $\newline$ C. $\sum_{i=1}^{88} 2.5(1.2)^{k}$ $\newline$ D. $\sum_{i=1}^{88} 2.5(1.2)^{k-1}$

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Find derivatives of using multiple formulae

Full solution

Q. What is this series witten in sigma notation?

\newline

2.5+2.5(1.2)+2.5(1.2)^{2}+\ldots+2.5(1.2)^{87}

\newline

A.

\sum_{i=1}^{87} 2.5(1.2)^{k}

\newline

B.

\sum_{i=1}^{8 \pi} 2.5(1.2)^{k-1}

\newline

C.

\sum_{i=1}^{88} 2.5(1.2)^{k}

\newline

D.

\sum_{i=1}^{88} 2.5(1.2)^{k-1}

Identify terms and ratio: Identify the first term and common ratio of the series. $\newline$ The first term is $2.5$ , and the common ratio, $r$ , is $1.2$ since each term is multiplied by $1.2$ to get the next term.
Write in sigma notation: Write the series in sigma notation. $\newline$ The series starts at $2.5$ and each subsequent term is the previous term multiplied by $1.2$ . The series can be written as: $\newline$ $\sum_{i=0}^{87} 2.5 \cdot (1.2)^i$
Check options for match: Check the options given to match the sigma notation. $\newline$ Option A: $\sum_{i=1}^{87} 2.5(1.2)^{k}$ - Incorrect because it starts from $i=1$ and uses $k$ instead of $i$ . $\newline$ Option B: $\sum_{i=1}^{8\pi} 2.5(1.2)^{k-1}$ - Incorrect because it uses $8\pi$ as the upper limit and $k-1$ . $\newline$ Option C: $\sum_{i=1}^{88} 2.5(1.2)^{k}$ - Incorrect because it starts from $i=1$ and goes to $88$ . $\newline$ Option D: $i=1$ $0$ - Correct, it adjusts for the starting index of $i=1$ $1$ by using $k-1$ and correctly goes up to $88$ terms.

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