Inspired By Sharky Kesa

Calculus Level 5

$\large \sum_{n=2}^{\infty} \dfrac{\zeta(n)+\zeta(2n)}{n!} = \, ?$

Notation : $\zeta(\cdot)$ denotes the Riemann zeta function .

Inspiration .

The answer is 1.8407.

1 solution

K T
Nov 11, 2019

It converges very rapidly, so numerical approach is easy

import math;

def zeta(k):
    i=1;
    sum=0;
    f=math.log(k);
    term=1;
    sum=1;
    while term > 1E-10:
        i+=1;
        term = i**(-k);
        sum += term;
    return sum;

def determine():
    sum=0;
    term=1;
    k=1;
    while term>1E-10:
        k+=1;
        term =(zeta(k)+zeta(2*k))/math.factorial(k);
        sum+=term;
    return sum;

print(determine());

Inspired By Sharky Kesa

The answer is 1.8407.

1 solution

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