I cannot figure out which ones are true and which ones are false!! If you can help me please do!! Thanks!
An infinite geometric series will converge if the associated geometric sequence has a limit of 0.
All infinite arithmetic series diverge.
An infinite sum is equal to the limit of the associated sequence.
Suppose an is an arithmetic sequence with d > 0. Then the sum of the series a1+a2+a3+...a12 must be positive.
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1)true sum q^n converge if IqI<1 and then q^n===>0
2)true S _n= na+(n-1)*n*r/2 ==> infinity
3)false the sum of q^n is 1/(1-q) and q^n===>0 (see 1)
4) d=r S_12 = 12a1+11*12/2*d =12a1+66 d and the sign of the sum of the 12 terms depends on a1
Look at 2) if n==>infinity the dominant term is n^2d/2 >0