Find the sum of the infinite series whose sequence of partial sums, Sn, is 

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Hello!

So, store in mind that what we mean Sn. It is what we acquire after adding together the first n regards to some sequence an. So, for example, if we had actually a sequence of terms that we wanted to add together, let"s say it"s an=1 (that is, every member of the sequence is 1), we have the right to uncover it"s sequence of partial sums Sn. To list a few, S1 = 1, S2= 1+1, S3=1+1+1, and so on. You"d check out that Sn = n. So if we wanted to discover the unlimited sum of an, we would take the limit of Sn. (In this instance instance, we"d be doing limn->∞n, and given that this limit doesn"t exist, we say the boundless series does not converge, or diverges...in other words, if you include 1+1+1+1+1...forever, it does not converge to any value: rather intuitive!).

You are watching: Calculate the sum of the series whose partial sums are given

Now, ago to your problem! If your partial sums are provided by Sn= 10 - 1/(n+1), then all we desire to carry out is take the limit of Sn.

Thus your answer is:

limn-->∞Sn = limn-->∞(10 - 1/(n+1)).

= limn-->∞10 - limn-->∞(1/(n+1))

=10 -0

=10.


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