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Sum of series/ 1+x+x2+x3+

Sum of series 1+x+x2+x3+


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  )   (1 + x + x2 + x3)
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n = 1
∑n=1∞(x3+(x2+(x+1)))\sum_{n=1}^{\infty} \left(x_{3} + \left(x_{2} + \left(x + 1\right)\right)\right) 
Sum(1 + x + x2 + x3, (n, 1, oo))
The radius of convergence of the power series
Given number:
x3+(x2+(x+1))x_{3} + \left(x_{2} + \left(x + 1\right)\right)
It is a series of species
an(cx−x0)dna_{n} \left(c x - x_{0}\right)^{d n}
- power series.
The radius of convergence of a power series can be calculated by the formula:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=x+x2+x3+1a_{n} = x + x_{2} + x_{3} + 1
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞11 = \lim_{n \to \infty} 1
Let's take the limit
we find
True

False
The answer [src] 
oo*(1 + x + x2 + x3)
∞(x+x2+x3+1)\infty \left(x + x_{2} + x_{3} + 1\right) 
oo*(1 + x + x2 + x3)

    Examples of finding the sum of a series

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