Mister Exam

### Other calculators

• #### How to use it?

• Sum of series:
• (1)/(2^n+n)
• k^2*x-12*k^14-2*x
• nx^n
• 1/((1+r)^n)
• #### Identical expressions

• (one)/(two ^n+n)
• (1) divide by (2 to the power of n plus n)
• (one) divide by (two to the power of n plus n)
• (1)/(2n+n)
• 1/2n+n
• 1/2^n+n
• (1) divide by (2^n+n)

• (1)/(2^n-n)

# Sum of series (1)/(2^n+n)

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### The solution

You have entered [src]
  oo
____
\
\      1
\   ------
/    n
/    2  + n
/___,
n = 1       
$$\sum_{n=1}^{\infty} \frac{1}{2^{n} + n}$$
Sum(1/(2^n + n), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{2^{n} + n}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = \frac{1}{2^{n} + n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{2^{n + 1} + n + 1}{2^{n} + n}\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
0.697276598391672325964864622083
0.697276598391672325964864622083`