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

limn-->∞Sn = limn-->∞(10 - 1/(n+1)).

= limn-->∞10 - limn-->∞(1/(n+1))

=10 -0

=10.

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