1) Using Std2 - Cos[something illegible], calculate:
a) \(\displaystyle \displaystyle \lim _{m\to 0}\left(\frac{1+\sqrt{2}+\sqrt{3}+...+\sqrt{m}}{m\sqrt{m}}\right)\)
b) \(\displaystyle \displaystyle \lim _{m\to 0}\left(\frac{ln\left(1\right)+ln\left(2\right)+ln\left(3\right)+...+ln\left(m\right)} {ln\left(m\right)}\right)\)
\(\displaystyle ln = log_10\)
2) Using D'Alembert [naport?] [oreterium?], calculate:
\(\displaystyle \displaystyle \lim _{m\to \infty }\left(x_m\right)=?\)
a) \(\displaystyle x_m=\dfrac{S^n}{m!}\)
b) \(\displaystyle x_m=\dfrac{2^m+2 \cdot 3^m + 3 \cdot 5^m}{3^m+ 3 \cdot 4^m + 5 \cdot 5^m}\)
3) Convergent/Divergent
a) \(\displaystyle a_m=\dfrac{1}{2\cdot5}+\dfrac{1}{3\cdot6}+\dfrac{1}{4\cdot7}+...+\dfrac{1}{(m+1)(m+4)}\)
b) \(\displaystyle b_m=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{m(m+1)}\)