Find the amount of the infinite collection whose sequence of partial sums, Sn, is 

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Hello!

So, keep in mind that what us mean Sn. It is what we acquire after including together the an initial n terms of some succession an. So, for example, if we had a succession of terms that we wanted to include together, let"s speak it"s an=1 (that is, every member the the succession is 1), us can find it"s succession of partial sums Sn. To list a few, S1 = 1, S2= 1+1, S3=1+1+1, and so on. You"d watch that Sn = n. Therefore if we wanted to discover the infinite sum the an, we would take the limit the Sn. (In this instance case, we"d it is in doing limn->∞n, and also since this limit doesn"t exist, us say the infinite collection does not converge, or diverges...in various other words, if you include 1+1+1+1+1...forever, the does not converge to any kind of value: quite intuitive!).

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

Now, back to your problem! If her partial sums are offered by Sn= 10 - 1/(n+1), then all we desire to do is take it the limit of Sn.

Therefore your answer is:

limn-->∞Sn = limn-->∞(10 - 1/(n+1)).

= limn-->∞10 - limn-->∞(1/(n+1))

=10 -0

=10.


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