制限
$$ lim _ { Delta x to 0} frac { arctan left( dfrac { Delta x} {1 + x(x + Delta x)} right)} { Delta x} = lim _ { Delta x to 0} frac { arctan left( dfrac { Delta x} {1 + x ^ 2}
$ def e { mathrm {e}} $ $ n in mathbb {N} _ + $の場合、$$ S_n = sum_ {k = 0} ^ n binom {n} {k}( 1 + e ^ {-(k + 1)})^ {n + 1}、 T_n = sum_ {k = 0} ^ n binom {n} {k}(1 +