Questions: -3+5-7+9-11+13-15= sum from n=1 to A of B, where A= B=

-3+5-7+9-11+13-15= sum from n=1 to A of B, where A= B=
Transcript text: -3+5-7+9-11+13-15=\sum_{n=1}^{A} B, where $A=$ $\square$ $B=$ $\square$
failed

Solution

failed
failed

Solution Steps

To express the given sum using sigma notation, we need to identify the pattern in the sequence and determine the general term. The sequence alternates between positive and negative numbers and increases by 2 each time. We can use this pattern to find the general term and the number of terms in the sequence.

Step 1: Identify the Sequence

The given sequence is \(-3, 5, -7, 9, -11, 13, -15\). We observe that the terms alternate in sign and increase in absolute value by 2.

Step 2: Determine \( A \)

The number of terms in the sequence is \( A = 7 \).

Step 3: Establish the General Term \( B \)

The general term can be expressed as: \[ B = (-1)^{n+1} (2n - 1) \] This formula captures the alternating signs and the increasing odd numbers.

Final Answer

Thus, we can express the sum using sigma notation as: \[ -3 + 5 - 7 + 9 - 11 + 13 - 15 = \sum_{n=1}^{7} (-1)^{n+1} (2n - 1) \] The values are: \[ A = 7, \quad B = (-1)^{n+1} (2n - 1) \] The final boxed answer is: \[ \boxed{A = 7, \, B = (-1)^{n+1} (2n - 1)} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Temporary, widespread vasodilation and syncope caused by a sudden nervous system reaction MOST accurately describes: Select one: A. vasovagal shock. B. neurologic shock. C. psychogenic shock. D. neurogenic shock. To protect vital organs, the body compensates by directing blood flow away from organs that are more tolerant of low flow, such as: Select one: A. the brain. B. the lungs.
failedAnswered
The graph of y=f(x) is shown to the right. Identify the x-coordinates of the points where f(x) has a local minimum. Which of the following shows every x-coordinate where f(x) has a local minimum? Choose the correct answer below. A. a, d, 9 B. a, c, 9 C. d, g D. b, 1
failedAnswered
Smith, who has 10,000, receives an extra dollar, as does Jones, who has 100,000. Smith receives more utility from the extra dollar than does Jones. This is an example of an interpersonal utility comparison. the law of diminishing marginal utility. the diamond-water paradox. a and b
failedAnswered
A. For tap water, the mode pH is . (Round to three decimal places as needed. Use a comma to separate answers as needed.) B. There is no mode.
failedAnswered
Determine the period of the function (y=cos left(-frac14 xright)) and sketch its graph. Choose the correct graph of (y=cos left(-frac14 xright)) below. A. B. C. D.