To explain why an arithmetic series is always divergent.
Answer to Problem 67HP
An arithmetic series is always divergent
Explanation of Solution
Given:
An infinite arithmetic series.
Concept Used:
Sum of first n terms of an arithmetic series whose first term is a and common difference d is:
Calculation:
To explain why an arithmetic series is always divergent.
First consider an infinite arithmetic series
Then sum of its n term is given by the formula:
Note that both the terms of above sum tends to infinity as n tends to infinity, i.e.
Thus, the above sum diverges a n tends to infinity, since
Thus, an arithmetic series is always divergent.
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