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October 11th, 2012, 08:06 PM  #1 
Newbie Joined: Oct 2012 Posts: 1 Thanks: 0  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. 
October 12th, 2012, 04:16 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,958 Thanks: 1845 
1. True 2. False 3. True 4. False 
October 12th, 2012, 04:10 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625  Re: Sequences and series. True or false?
4. is true for r < 1: answer is a/(1r), where a is the first term.


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