Question 1061950
This series is known as Euler's Series.  The solution is not trivial and fairly lengthy regardless of approach.   Here is a paper where the author discusses six different solutions, each using a different approach.   A few justifications are missing here and there but in the end, they all reach the correct result.

https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020759.02p00026.pdf