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October 11th, 2012, 07:06 PM   #1
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Sequences and series. True or false?

Can anybody help me determine wether or not these statements are true or false? I've tried multiple combinations and can't get it right. :/

1. All infinite arithmetic series with d not equal to 0 diverge.

2. Suppose an is an arithmetic sequence with d0. Then the sum of the series a1+a2+a3+...+a12 must be positive.

3. An infinite sum is equal to the limit of the sequence of partial sums.

4. An infinite geometric series must converge if r<1.
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October 12th, 2012, 03:16 AM   #2
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1.  True
2.  False
3.  True
4.  False
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October 12th, 2012, 03:10 PM   #3
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Re: Sequences and series. True or false?

4. is true for |r| < 1: answer is a/(1-r), where a is the first term.
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