# What is the value of the infinite sum #1+(x+1) + (x+1)^2+ (x+1)^3 + ....# Given #abs(x+1)<1# ?

Sum

Thus, our infinite sum (S) in this example will converge to:

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do you use the integral test to determine if #Sigma arctann/(n^2+1)# from #[1,oo)# is convergent or divergent?
- How do you test the improper integral #int x/absxdx# from #[-5,3]# and evaluate if possible?
- How do you determine if the improper integral converges or diverges #int dx/((3x-2)^6) # from 2 to infinity?
- #sum_(n=0)^oo 5^n/(3^n +4^n)#. Does the series converge or diverge?

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