Consider the series ∑n=0∞54n. The sum of a series is defined as the limit of the sequence of partial sums, which means

(a) The n-th partial sum of the infinite series,

is

Multiplying both sides by 1/4 gives

Subtract this from and solve for :

(your solution is also correct)

(b) The infinite sum is equal to the limit of the n-th partial sum:

and the sum indeed converges to 20/3.

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered

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