Mister Exam

Lang:

Sum of series ln(k+1)/n

You have entered [src]

  oo            
 ___            
 \  `           
  \   log(k + 1)
   )  ----------
  /       n     
 /__,           
n = 1

\sum_{n=1}^{\infty} \frac{\log{\left(k + 1 \right)}}{n}

Sum(log(k + 1)/n, (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{\log{\left(k + 1 \right)}}{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{\log{\left(k + 1 \right)}}{n}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\frac{n + 1}{n}\right)

True

False

The answer [src]

oo*log(1 + k)

\infty \log{\left(k + 1 \right)}

oo*log(1 + k)