Approximate sum with Euler's contant

How do I approximate the lowest number of n with Euler's constant (0.577) so that the sum is greater than 14,3?

How do I after that calculate the exact value of n?

[Torsten]

Hint:

For n large, your sum is approximately eulergamma + log(n). Can you solve

eulergamma + log(n) = 14.3

for n ?

[Nathalie]

Yes, thank you! How do I calculate the exact value?

[John D'Errico]

Since you know ROUGHLY how far to go from the comment from @Torsten. Why not just form the sum using a while loop? You know that it will not go too far. Stop the while loop when it exceeds that amount. In fact, it will take only a moderately short loop. Or, you could use cumsum.

But you need to make an effort.

Answer 1

[Sulaymon Eshkabilov]

You may also try a symbolic math TB's function syms and solve(), e.g.:

syms x
Solution = solve(pi-sin(x)==1, x)

Solution = 

Solution_values = double(Solution)    % Get the solution values in double format

Solution_values = 
   1.5708 - 1.3951i
   1.5708 + 1.3951i