Question content area top part 1 use the limit as n...

Question content area top Part 1 Use the limit as n approaches infinity of the sum Upper S Subscript n to show that 2 plus 1 plus one half plus one fourth plus ... converges to 4. Question content area bottom Part 1 Find the expression for the sum of the first n terms of this sequence. Upper S Subscript n equals enter your response here (Do not simplify.)

Transcript

00:01 Hi, i'm david and i'm here to have you and send your question.

00:03 Here we have two questions, so let me do it one by one.

00:06 For the first question one, we want to find the summation on the 5 over the n times in the n plus 2 and form the 1 to infinity.

00:15 Notice that we can write this one into the form on the difference between the two fractions.

00:23 So the first one will be over the n, the other one will be n plus 2.

00:28 And now if we want to set up here, this one will be if we put the one and the one here, then we have that if we do the common denominator, we should get the n plus 2 minus the n which is equal to the 2, but 2 will be not the same as the 5.

00:45 Therefore i will multiply outside here will be the 5 out of 2 to cancel out the 2 and then we'll get back to the 5.

00:53 Therefore this one will get equal to the 5 out of 2.

00:57 Put it outside summation on the 1 out of n minus 1 out of n plus 2 from 1 to infinity.

01:04 Now it will have the 5 out of 2.

01:06 I will try to list out several quantity for the n equals 1 and then plus when the n equals 2 plus when the n equals to the 3 plus when the n equals to the 4 and so on.

01:23 Now for the first case on the n equals to the 1, we will have 1.

01:27 1 over 1 will be 1 minus 1 over 1 plus 2 will be the 3.

01:33 And then the next one will be 1 1 1.

01:36 1 out of 4...

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