A) [tex] \Sigma ^{5}_{i=1} (2i+1)^{2}[/tex]; Desarrollamos la sumatoria:
[tex]= (2(1)+1)^{2}+(2(2)+1)^{2}+(2(3)+1)^{2}+(2(4)+1)^{2}+(2(5)+1)^{2}[/tex]
[tex]= (2+1)^{2}+(4+1)^{2}+(6+1)^{2}+(8+1)^{2}+(10+1)^{2}[/tex]
[tex]= (3)^{2}+(5)^{2}+(7)^{2}+(9)^{2}+(11)^{2}[/tex]
[tex]= 9+25+49+81+121[/tex]
[tex]=285[/tex]
Por tanto: [tex] \Sigma ^{5}_{i=1} (2i+1)^{2}=285[/tex]
B) [tex] \Pi ^{4}_{i=1} \frac{i}{i+1} [/tex] ; Desarrollamos la Multiplicatoria:
[tex] \Pi ^{4}_{i=1} \frac{i}{i+1} = (\frac{1}{1+1})(\frac{2}{2+1})(\frac{3}{3+1})(\frac{4}{4+1}) [/tex]
[tex]=(\frac{1}{2})(\frac{2}{3})(\frac{3}{4})(\frac{4}{5})[/tex] ; Simplificando:
[tex]=(\frac{1}{1})(\frac{1}{1})(\frac{1}{1})(\frac{1}{5})[/tex]
[tex]= \frac{1}{5} [/tex]
Por tanto: [tex]\Pi ^{4}_{i=1} \frac{i}{i+1}= \frac{1}{5} [/tex]
