In Exercises 61–68, use the graphs of and to find each indicated sum.∑i=45(ai/bi)3\sum_{i=4}^5(a_{i}/b_{i}$$)^3$$

Ch. 8 - Sequences, Induction, and Probability

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Blitzer 8th Edition

Ch. 8 - Sequences, Induction, and Probability

Problema 66

Capitolo 9, Problema 66

In Exercises 61–68, use the graphs of and to find each indicated sum.

$\sum_{i = 4}^{5} (a_{i} / b_{i})^{3}$

Guida verificata passo dopo passo

Step 1: Identify the values of the sequences $a_n$ and $b_n$ for $n = 4$ and $n = 5$ from the graphs. For $a_n$, locate the points at $n=4$ and $n=5$ on the first graph and note their corresponding $a_n$ values. For $b_n$, do the same on the second graph.

Step 2: Write down the values you found for each $n$. For example, $a_4$, $a_5$, $b_4$, and $b_5$.

Step 3: Calculate the ratio $\frac{a_i}{b_i}$ for each $i = 4, 5$. This means dividing the value of $a_i$ by the value of $b_i$ for each index.

Step 4: Cube each ratio found in Step 3, i.e., compute $\left(\frac{a_i}{b_i}\right)^3$ for $i = 4, 5$.

Step 5: Sum the cubed ratios for $i = 4$ and $i = 5$ to find $\sum_{i=4}^5 \left(\frac{a_i}{b_i}\right)^3$.

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