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Evaluate the sum f the series(-lyn+l x2n+8 7nnl n =0at x = 1 ....

Question

Evaluate the sum f the series(-lyn+l x2n+8 7nnl n =0at x = 1 .

Evaluate the sum f the series (-lyn+l x2n+8 7nnl n =0 at x = 1 .



Answers

Find the sum of each series.
$\sum_{n=0}^{3} \frac{1}{n !}$

Okay, so it's no that. And really, that's not what's wrong and ends at three. So it's ex friend. Do we have that extra power of zero cost? Want what you want, plus negative X to the power of one plus one, which is to negative extra power of Well, sorry about that. So this is a factory, and then we have negative excutive power of three plus one, which is four. And that's our last time. Now let's expand what we have and they have X cubed and lastly, X to the power of four. Okay, so this is our following summation.

Okay, fund this Some of the Siri's s. So this is Look, this looks very similar to our exponential function. But of course, we're gonna do some, like some change wearables to make it look similar to eat a power X. So is this him too? And from zero to Philly and minus one times except for four to the powers in Over in factorial. And let's see if we change t equals not you extra port for And this is just so it is Pete to the poor tea. So it was to eat. Report, Not you. Oh four. And this is our results. Shakespeare. Nothing. That's two for four.

This finest Cem off. Uh, this guy right here. So to find us some we can make it. We can do it many ways, but it simply isn't a shortest way as toe try to manipulate this one. It's one of thes standard Siris for from the tables. Rain s So what does this one looks like it loose. It looks somewhat like this. Eat to the x ray. Looks like either the ex This is e to the x. At least a denominator. Have something same here at in greater. I'm just missing for So it is up to me to manipulate, uh, things to make sure I get something. And I didn't have this negative, but I can do that. If I may hear negative. And this is gonna be It means that we're I see an instance off X. I should replace it by negative X. Right. So this is gonna be negative ecstasy in over in factory. And that, in fact, about a negative one. There's a negative. This is a negative one, right? Just a negative. What? I can fracture it out. So when I find threw that out, then this is gonna be summation in from zero to infinity. Negative one to the end. That is factory negative. One out from here is gonna carry this in a way, right? The status factory. And then I'm gonna have my extra in left over. So you see that now? By changing here to negative, I've been able to achieve this negative one here. Right? So what is left for me to achieve its this four. Right. So how can I see that for it means that I wouldn't write. See an instance of eggs as she just replace it by Excellent. Four. Right. That is how I'm gonna achieve that. So then this one is gonna be negative One city. And now you see an X here, so I'm gonna replace it by accident. Four. So just gonna be exit for in order. In fact, you're it right? And there's finally gonna be summation. Negative wants it. And it's just pure manipulation right now. Look, it's just just it's just the same as this one. Does it seem like this one? They have. What is some of this one is, uh, e to the negative x, uh, exit of four. Right. So that's it So simple. It's just pure


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