Q. 6 Explain why the sequence of part... [FREE SOLUTION]

Chapter 7: Q. 6 (page 614)

Explain why the sequence of partial sums of the series ${鈭�}_{k = 1}^{鈭�} a_{k}$ in which $a_{k} > 0$ for every $k 鈭� {鈩�}^{+}$ is strictly increasing.

Short Answer

Expert verified

The sequence of partial sums of a series ${鈭�}_{k = 1}^{鈭�} a_{k}$ s the partial sum of the first through nth terms.

The sequence of partial sums is given by, $\{S_{n}\} = \{a_{1}, (a_{1} + a_{2}), . . ., (a_{1} + a_{2} + . . . + a_{n})\}$ . As each $a_{k} > 0$ .

The sequence of partial sums of the given series is strictly increasing.

Step by step solution

Step 1. Given information.

Consider the given question,

The series ${鈭�}_{k = 1}^{鈭�} a_{k}$ in which $a_{k} > 0$ .

Step 2. Explain the sequence of partial sums of the given series.

The sequence of partial sums of a series ${鈭�}_{k = 1}^{鈭�} a_{k}$ is the partial sum of the first through nth terms.

It can be defined as, $S_{n} = a_{1} + a_{2} + . . . + a_{n}$ .

The sequence of partial sums is given by,

$\{S_{n}\} = \{{鈭�}_{k = 1}^{n} a_{k}\} = \{a_{1}, (a_{1} + a_{2}), . . ., (a_{1} + a_{2} + . . . + a_{n})\}$

As each $a_{k} > 0$ .

Therefore, the sequence of partial sums of the series ${鈭�}_{k = 1}^{鈭�} a_{k}$ is strictly increasing.

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Explain why the sequence of partial sums of the series ${鈭�}_{k = 1}^{鈭�} a_{k}$ in which $a_{k} > 0$ for every $k 鈭� {鈩�}^{+}$ is strictly increasing.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explain the sequence of partial sums of the given series.

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91影视

Explain why the sequence of partial sums of the series 鈭�k=1鈭�akin which ak>0for every k鈭�鈩�+is strictly increasing.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Explain the sequence of partial sums of the given series.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Pure Maths

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

Explain why the sequence of partial sums of the series ${鈭�}_{k = 1}^{鈭�} a_{k}$ in which $a_{k} > 0$ for every $k 鈭� {鈩�}^{+}$ is strictly increasing.