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Write the series using summation notation. Then find the sum of the series.

1 + 2 + 3 + ++ + 12

And

1/2 + 1/4 + 1/6 + ++ + 1/14

Respuesta :

Alfpfeu

Hello, please consider the following.

[tex]\displaystyle 1+2+3+...+12=\sum_{k=1}^{k=12} {k}=\dfrac{12*13}{2}=6*13=78[/tex]

For the second we will need to put on the same denominator.

[tex]\displaystyle \dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{14}=\sum_{k=1}^{k=7} {\dfrac{1}{2k}}\\\\=\dfrac{1}{2}\dfrac{420+210+140+105+84+70+60}{5*7*3*2*2}\\\\=\dfrac{1}{2}\dfrac{1089}{420}\\\\=\dfrac{1089}{840}=1.296429...[/tex]

Thank you.

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