Please allow me to quote André Weil twice. First, from page 27 of The Apprenticeship of a Mathematician, concerning his first form teacher, Monsieur Collin:
'There was a strong temptation to take short-cuts, saying "it is obvious that..."; Monsieur Collin taught me never to use this word. "If it were obvious," he said, "you would not feel the need to say so; if you say so, that means it is not obvious." He is the one who taught me how to write up mathematics.'
The second quote, from page 19 of Elliptic Functions According to Eisenstein and Kronecker:
"Combining the above formulas, we get for all $n\geq 1$, the following series for $E_n(x)$: $$E_n(x) = u^{-n} \sum_{v=-N}^{+N}\epsilon_n(\zeta + v\tau)+\frac{(2\pi/iu)^n}{(n-1)!}\sum_{v=N+1}^{+\infty}\sum_{d=1}^{+\infty}d^{n-1}q^{vd}[z^d+(-1)^nz^{-d}]$$ where the double series is easily seen to be absolutely convergent provided $N$ has been taken such that $|q^{N+1}z|<1$ and $|q^{N+1}z^{-1}|<1$."
I will refrain from the obligatory of course joke and leave the moral of the story as an exercise instead.