Chapter 7: Q 44. (page 615)

Given that $a_{0} = - 3, a_{1} = 5, a_{2} = - 4, a_{3} = 2$ and ${\sum a_{k}}_{k = 2}^{\infty} = 7$ , find the value ofrole="math" localid="1648828282417" ${\sum a_{k}}_{k = 1}^{\infty}$ .

Short Answer

Expert verified

The value of ${\sum a_{k}}_{k = 1}^{\infty} = 12$ .

Step by step solution

Step 1. Given information.

Given that $a_{0} = - 3, a_{1} = 5, a_{2} = - 4, a_{3} = 2$ and ${\sum a_{k}}_{k = 2}^{\infty} = 7$ .

Step 2. Express the series in terms of known values.

Value of ${\sum a_{k}}_{k = 1}^{\infty}$ can be obtained as follows.

$\begin{array}{rcl} {\sum a_{k}}_{k = 1}^{\infty} & = & a_{1} + {\sum a_{k}}_{k = 2}^{\infty} \\ = & 5 + 7 \\ = & 12 \end{array}$

Therefore, value of ${\sum a_{k}}_{k = 1}^{\infty}$ is 9.

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Given that $a_{0} = - 3, a_{1} = 5, a_{2} = - 4, a_{3} = 2$ and ${\sum a_{k}}_{k = 2}^{\infty} = 7$ , find the value ofrole="math" localid="1648828282417" ${\sum a_{k}}_{k = 1}^{\infty}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Express the series in terms of known values.

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Given that a0=-3,a1=5,a2=-4,a3=2and ∑akk=2∞=7, find the value ofrole="math" localid="1648828282417" ∑akk=1∞.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Express the series in terms of known values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Discrete Mathematics

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Calculus

Study anywhere. Anytime. Across all devices.

Given that $a_{0} = - 3, a_{1} = 5, a_{2} = - 4, a_{3} = 2$ and ${\sum a_{k}}_{k = 2}^{\infty} = 7$ , find the value ofrole="math" localid="1648828282417" ${\sum a_{k}}_{k = 1}^{\infty}$ .