Determine if the series is convergent or divergent -5+25-125+....
1 answer:
Answer:
b)Divergent
Step-by-step explanation:
Given is a series
-5+25-125+....
We find that this is following a pattern such that each term is multiplied by -5 to get the next term
In other words, this series is a geometric series with common ratio r =-5 and I term a=-5
Since sum of n terms of geometric series =
Since |r|=|-5|>1, we find that this sum tends to infinity or -infinity as n tends to infinity
In other words, the series diverges
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First step, divide 6 from both sides.
t/6=r^2+1
second step, subtract 1 from both sides
t/6 -1=r^2
Now take the square root of each side.
Done!