Limit[((Sin[(x^n)]  -  (x^n))/(x^(3  n))) /. n -> 100, 
      x -> 0]

Limit[(((n + 1))^(1/2))  -  (n^(1/2)),  n -> ∞]

Limit[(x^(1/(1 - x))), x -> 1]

Sum[(x^n), {n, k, ∞}]

Sum[((((2^n) - 1) ((2^n) + 1))/(5^n)), {n, 1, ∞}]

Sum[(1/(4 n^2 - 1)),{n, 1, ∞}]

NSum[((((-1))^(n - 1))/(n^(1 + 1/n))), {n, 1, ∞}]

NSum[(1/(n^(1 + 1/n))), {n, 1, ∞}]

NSum[((n!)/(n^n)), {n, 1, ∞}]

NSum[n (((-π))^(-n)), {n, 1, ∞}]

NSum[n  (π^(-n)), {n, 1, ∞}]

t  =  
      Table[Sum[N[((((Sqrt[n]) +  (((-1))^n) n))/(n (Sqrt[ n])))], {n, 2, m}], 
         {m, 2, 100}];

ListPlot[t]

ListPlot[
      Table[Abs[N[((((Sqrt[n]) +  (((-1))^n) n))/(n (Sqrt[ n])))]], 
         {n, 2, 100}]]

NSum[((((Sqrt[n]) +  (((-1))^n) n))/(n (Sqrt[ n]))), 
       {n, 2, ∞}]

Series[(x^2) Sin[x] - Sin[(x^3)], {x, 0, 5}]

Series[(((x^2) Sin[x] - Sin[(x^3)])/(x^5)), {x, 0, 5}]

f[x_]  :=  1/(x^(1 + 1/x))

Plot[f[x], {x, 1, 10}]

f'[x]  // Simplify