Determine wheter the infinite geometric series coverges or diverges. If it covereges, find its sum
Infinite geometric series:
Condition 1:
An infinite geometric series converges if and only if ''the value of common ratio is less than 1'' ( r <1). In this case, sum of the series is equal to a1/(1-r) where a1 is the first term and r is the common ratio.
Condition 2:
An infinite geometric series diverges if the value of common ratio is more than 1 ( r >1). In this case, sum of the series
has no limit and the sum approaches infinity.
Infinite arithmetic series:
The sum of an infinite arithmetic series is either +∞, if d=positive, or - ∞, if d=negative where d is common difference.
Because the sum of infinite arithmetic series approaches infinity, therefore the infinite arithmetic series diverges.
Any other series:
If the sum of any series approaches infinity then the series diverges.
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