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1 unskensWhhich Tha 22 curyo I # 1 Sudo Jonmnba (ollotano oinar (0) Support your answer by graphirg of the potynomtal oeorod and the 3 1 Jopons benavior onthn L aoi...

Question

1 unskensWhhich Tha 22 curyo I # 1 Sudo Jonmnba (ollotano oinar (0) Support your answer by graphirg of the potynomtal oeorod and the 3 1 Jopons benavior onthn L aoing polnomliTunclon li rght because Ihc Ioading iw N tuncuol { L 1 corcantis 1 llo Bcau 90 1E

1 unskens Whhich Tha 22 curyo I # 1 Sudo Jonmnba (ollotano oinar (0) Support your answer by graphirg of the potynomtal oeorod and the 3 1 Jopons benavior onthn L aoing polnomliTunclon li rght because Ihc Ioading iw N tuncuol { L 1 corcantis 1 llo Bcau 90 1 E



Answers

(n-1)!(n2+n)

Hi friends. As soon as the figure A. And B. For A. You can write to to death is equal to cp into peanut 1 -1 upon it. And Cuban does Cuban double necessary can be written as are we not? None of And Cuban desk and get a nice CVT not one minus burn upon end and Cuban can readiness Cuban days plus Q. Wonderfulness. Hence its efficiency can be written as 1 -62 days upon Cuba. That is one CP into 1 -1 apart and divided by c. v. into 1 -1 opponent plus are no no end simplifying it. You can write efficiency to me when minus comma times. And my new husband here gamma is cp upon CV and uh minus one plus gamma minus one into and Lana van no figure to be four figure be Cuban baby C. P. D. Not and minus went yeah cute to double death. Will we see the do you not? And my husband Q two triple this will be are we not learn of and and you two days will be to to double days and Q 2 to pull this So efficiency. You can define one Q. two days over Cuba. That has been minus and minus one Because we come out my next one None of end the gradual gamma into N -1. That's thanks for watching it

So this is basically question and as you can see this follows a pattern. So like to get to 12 negative two you will have to do up negative, you will have to add a negative three. To get to negative to the negative day you have to add a negative one. So then the pattern is going from plus two. So if he plus two with negative one that will make it one. So this will be negative too because negative two plus one is negative one. As you can see when we add 2 to 1 that would give us three. So now here it should be five. What gives us five? So should be negative five here as you can see 32 So this gives us one. Oh I think I made a mistake. So it's negative three negative 113 And now it goes back to uh negative three. So we write negative three here so we make same and then uh it's going to be negative one and that's how you finished it. Thank you. Hope this helps

That one is square plus two square plus. There's a series is it's up to and square. So the some of the series should be equal to one plus two plus don't tell in light is square and that is for all positive in teachers. And so let us just prove this. So I'm just going to prove this by the induction method. Now the base case says uh that one cube is equal to one this way, isn't it? This is true, Right? So uh I suppose the statement calls for in right? So suppose the statement whose foreign is like one Q plus two Q plus dot dot dot plus en Q. This was a Yeah thank you is equal to one plus two plus C. Up to n right square find brian saying this because uh by induction method one Q equal to a one square is true. So let us say that the series one Q plus two two Q plus up to n Q is equal to one plus two plus up to end whole squares. Right? So this will be equal to what? This is equal to end times and last one upon two whole square. Right now, why everything? This This tone has come from this I'm talking about this time. So this town follows from one plus two plus up til en. That is equal to end times in the last one upon two jake. So this whole thing is equal to and and plus one. I'm going to so there's a square. So I just put a square on the top. Right? So up till now this thing is clear. Now we now approved the statement for N plus one. Okay, so well now I have the spittle and now I'm going to do it till end plus one. So that means one Q plus two Q plus say up to thank you. Ok plus en Q. And plus there's another term that is N plus one Q. So this will be equal to what? This will be equal to N. N plus one are born two full square plus and plus one cute. Right? That will be equal to if you just uh like open out of these two terms what you'll get simply the one upon to works with that is one upon food then N plus one square. Then what? You'll get any square plus four times off and plus one. Right. So we caught up till now. Now this can be further simplify. So if I simplify this term, what I'm going to get is simply I can say one upon four N plus one square into any plus two whole square, isn't it? And this is equal to what this is equal to N plus one in two. N plus two Upon do this way. See I'm just simplifying this for then photo and this is for the equal to what this is for the equal to one plus two plus two plus en plus another time. That was N plus one right old square. So as you can see where here the induct does the induction step over here is also proven and the claim is true. Hence the series. This is true right? Hence I left. So this is how you can prove them giving a statement over here.

Okay here, the first step is to factories the second bracket into N and plus one. Now. I can write this then as N plus one, times and Times and -1 factorial. And that is M plus one. And the pattern you can see now is simply the factorial pattern. You take away one every time and you keep going down until you reach three two one. And that is the same as saying N plus one factorial, and that's the answer In this case and plus one factorial.


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