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

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.

limn-->∞Sn = limn-->∞(10 - 1/(n+1)).

= limn-->∞10 - limn-->∞(1/(n+1))

=10 -0

=10.

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