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Find the sum, if it exists, of the infinite geometric series = 102+112. 2+123. 42+…

User Karruma
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1 Answer

15 votes
15 votes

Answer:

it does not exist

Explanation:

if it is a geometric sequence, there must be a common ratio or multiplication factor between neighboring terms :

102 × r = 112.2

r = 112.2/102 = 1.1

is 112.2 × 1.1 = 123.42 ?

yes.

so, it is a geometric sequence with the common ratio of 1.1.

the problem is now : the ratio is > 1.

that means the sequence tends are growing, and growing, and the sum is therefore rather "exploding" than converging.

for the sum to converge to a specific number the individual terms need to get smaller and smaller in absolute numbers.

with r > 1 this is impossible, so there is no sum for this sequence (with n going to infinity, so does the sum, and as "infinity" is not a value per se, the sum does not exist).

User Grrussel
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