For What Values of P Does the Series $1+9 p+(9 p)^{2}+(9 p)^{3}+\ldots+(9 p)^{n}+$

question 31

Multiple Choice

For what values of p does the series $1+9 p+(9 p) ^{2}+(9 p) ^{3}+\ldots+(9 p) ^{n}+$ converge, if any?

• A) \(\frac{-1}{9}\)\(<\)\(p<\)\(\frac{1}{9}\)
• B) \(\frac{-1}{18}\) \(<\)\(p<\)\(\frac{1}{18}\)
• C)-1 < p < 1
• D) \(-1 \leq p \leq 1\)
• E)The series diverges for all values of p.

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Definitions:

Capillaries

Tiny blood vessels that connect arteries and veins, facilitating the exchange of water, oxygen, carbon dioxide, and many other nutrients and waste substances between blood and tissues.

Mesenteric Vein

A vein that drains blood from the small intestine (and sometimes from the large intestine) into the portal vein of the liver.

Liver

An essential body organ that plays a crucial role in removing toxins, synthesizing proteins, and producing the biochemicals needed for digestion.

Intestines

The lower part of the digestive system where food is digested and absorbed into the body, comprised of the small and large intestines.