give-a-the-first-four-terms-of-the-sequence-for-which-a_n-is-given-and-b-the-first-four-terms-of--10

Question

Give (a) the first four terms of the sequence for which $a_{n}$ is given and $(b)$ the first four terms of the infinite series associated with the sequence.
$$a_{n}=\frac{1}{n}+\frac{1}{n+1}, \quad n=1,2,3, \dots$$

Tyler Moulton · Accepted Answer

we want to find the first four terms of the sequence in series for which is given for each term of the sequence is A. N equals one over N plus one over N plus one. And and is given as +123 and so forth. Therefore the first four terms of sequences series are found for a one, A two, A three and a four. So in order to first find the sequence terms, we need to note that defined each sequence terms. We simply plug in the corresponding value, and for a one we have 1/1 plus 1/1 +182 is defined similarly and so on. So we first have a one is 1/1 plus 1/1 plus one. As I mentioned, three halfs A two is one half plus one, third equals +56 Then we have a three equals one third +147 12 and +84 is 1/4 plus 1/5 equals 9 20. Now we can like the series. Remember that the series is that some of our a. M. For the first four terms of our series is given as the sum of our A one through a four or three half plus five, six plus 7, 12 plus 9/20.

Lily An · Answer

Okay, so I&#x27;m going to plug these in for the first for 1/4 term. So it&#x27;s one plus 11 plus two. That&#x27;s 1/6. I&#x27;ve got 12 plus 12 plus two. So that&#x27;s gonna be won over seven. It looks like does this was chew this. Oh, wait to live. Three times four. So 1/12. Um, I have three plus one. Just four on the three post to which is five have got 1/20. I&#x27;ve got four plus one, which is five and then four plus two, which is six. So that&#x27;s gonna be once if we had five and then six, so that&#x27;s gonna be

Ankit Gupta · Answer

Okay. Here. In this case, we just need to find the 1st 4 term of this sequence. In this case, the sequence is defined as the first time is equal to two. The anatomist defined us in his equals. Two A and minus one plus three. Okay, for all and greater than. But all right, so which means that is equal. Stupid Because And it&#x27;s positive. So when an easy close to two, we have a to Z equals two. You can see this is eight to minus one, which is even less and even values toe. So to place, we would simply comes or terrified. Okay, when anything close to three this becomes a three is equals to a to a plus street. Because this is just we&#x27;re using the previous value. All right, so not it devalues five. So the simply comes out to be five plus three, which is equals to it. Okay. And and is equals to four. This becomes a four is equals toe a three plus t know what is a 38 threes? Eight. So eight plus three would simply comes out to be. This is a place feeling eight plus three. So it leads to this simply comes out 11. Right on. When we put in musicals to fight, we have. If I was equals two, a four plus three or a four is 11 11. Place really simply comes out with 40. Okay, if I just write all the stumps in one go. The stumps are five, eight, 11 and 14. All right.

Lily An · Answer

so we want to find the 1st 4 terms. We just have to put that in some cough 1/1 square plus one, which is one of her two. I&#x27;ve got 1/2 squared plus two, which is +16 I got 1/3 squared, plus three, which is 1/12 and 1/4 squared plus four, which is one over.

Linh Vu · Answer

first home Because the First Amendment you wouldn&#x27;t really go too far up. And then the second time a Jew we could, you know, bring this term will be no foreign times three and then a month plus two Never We should get echoed You&#x27;re fronting and then a tree echo +23 times the previous time will be fun thing. That&#x27;s true. So you got eco June 42 44 Here I found we echo Ju three times 44 plus you And then we get a go Do three times 44 was too. I&#x27;m gonna go to 1 34 and then we need to find a term. And but in a different item we need the on Remus term. So we had to continue from a five now three times one from 34 less Jew and we go do three times one from and then just doing B for far, then a six week of June 3 times far on Fargas Jew. So times three Press Jew 121 for a seven echo 23 times 121 for us too. Times three. Press Jew Echo Jittery six phone for her father a eight echo jittery times 3644 But still. So I&#x27;m still I was sorry. Times Tables 23644 times three plus ju You gotta go do 9 10,034

Ankit Gupta · Answer

Okay. Here. In this case, the sequence is defined as the first time is equals to zero. The Entercom is defined us three less end times off a and minus one. Okay, on this result is I lived for all and greater than what? Which means the sequence is defined for n greater than which means been and is equals to do. You just have to find the next four dumps off the sequence. So Menendez equals two. We have a to Z equals 23 plus two times off. Because any stew and this is two minus one, which is one so two times off, Evans, with this simply three plus two times off. Zero, which is three. Okay, the end is equals to three. So when an musicals to three, we have a three is equals 23 times up on the stand. This is a few times off it because three minus one is to. So this is three times three plus three times off a to a value streets or nine less trees. 12. All right, and energy goes to four. We have a foot, is equal to three plus four times off a three right this e don&#x27;t get confused. This is a looks likes name, but this is a okay. Ah, Now this is three plus four times off a three or four times off. It&#x27;s be a three values to also do well for 48 48 best trees. Okay, someone living energy close to fight. We have a five is equals three plus five times off a four. OK, does the previous value three plus five times off? All right, five times off. 51 is 255. Okay, 250 vie, Plus please. 258. So we have the fifth. Um but I I mean this If it values, it was 2 55 the 50. It&#x27;s obvious if I just write all this time. Is that three to wealth 51 2 58 as the next four times for the sequence

Problem

Give (a) the first four terms of the sequence for…

Problem 8 Easy Difficulty

Give (a) the first four terms of the sequence for which $a_{n}$ is given and $(b)$ the first four terms of the infinite series associated with the sequence.
$$a_{n}=\frac{1}{n}+\frac{1}{n+1}, \quad n=1,2,3, \dots$$

Answer

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