1+(-1)n/n, Any Idea?
The nth term of the sequence is given; check whether the sequence is convergent or divergent.
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The sum over n=1..Infinity of the series whose terms are (x^n)/n is -ln[1-x].
Your series is 1+sum[n=1..Infinity, ((-1)^n)/n] = 1 - ln[1-(-1)] = 1-ln[2], approximately 0.30685. Thus, the sum of the terms you defined is definitely convergent.
ln[x] is the natural logarithm of x, but you know that.
Your series is 1+sum[n=1..Infinity, ((-1)^n)/n] = 1 - ln[1-(-1)] = 1-ln[2], approximately 0.30685. Thus, the sum of the terms you defined is definitely convergent.
ln[x] is the natural logarithm of x, but you know that.
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1+(-1)n/n
If we put n=infinity then the result is 1. So the sequence
converges and its limit is 1.
If we put n=infinity then the result is 1. So the sequence
converges and its limit is 1.
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0
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