Which of the Following Series Will, When Rearranged, Converge to Different

question 119

Multiple Choice

Which of the following series will, when rearranged, converge to different values?
1) $\sum _ { n = 1 } ^ { \infty } n ^ { - 1 }$
2) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } n ^ { - 1 }$
3) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } n ^ { - 2 }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

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Definitions:

Sensory Fibers

Nerve fibers that transmit sensory information from the peripheral sense organs to the central nervous system.

Motor Fibers

Motor fibers are nerve fibers that transmit impulses from the nervous system to muscles, causing them to contract and produce movement.

Sensory Root

The part of a spinal nerve that carries sensory information from the peripheral body parts back to the spinal cord.

Dorsal Root

The part of a spinal nerve that carries sensory neural information to the spinal cord from the peripheral organs.