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3 years ago

Evaluate the geometric series or state that it diverges. [infinity] Σ e^-5n n=0

Mathematics

1 answer:

Marianna [84]3 years ago

4 0

Answer:

sum = = 1 / ( 1-e^(-5) )

( 1.00678 to 5 decimals)

Step-by-step explanation:

Question: sum

[infinity]

Σ e^-5n

n=0

We note that this is a geometric series,

with n=0, e^(-5n) = e^0 = 1

with n=1, e^(-5n) = e^(-5)

with n=2, e^(-5n) = e^(-10)

...

Therefore the common ratio is r=e^(-5)

and the sum for a geometric series

a+ar+ar^2 + ... ar^N

=a(1-r^(N+1)) / (1-r)

=1(1-r^(infinity-1)) / (1-e^(-5))

= 1 / ( 1-e^(-5) )

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