I need help with a homework assignment:

Write each series in summation notation beginning with k = 1.

1/2 + 2/3 + 3/4 + 4/5 + 5/6


−11 + 12 − 13 + 14 − 15 + 16

9 − 16 + 25 − 36 + 49 − 64

3 + (3/2) + 1 + (3/4) + (3/5)

I get the numbers that go under and on top of the sigma, I need help deriving the explicit value for the sequence that goes on the right of the sigma.
Thanks

Respuesta :

[tex]\bf \cfrac{1}{2},\cfrac{2}{3},\cfrac{3}{4},\cfrac{4}{5},\cfrac{5}{6}\qquad \sum\limits_{k=1}^5\ \cfrac{k}{k+1} \\\\\\ -11,12,-13,14,-15,16\qquad \sum\limits_{k=1}^6\ (-1)^k(k+10)\\\\ -------------------------------\\\\ \begin{array}{lllllllllll} 9&,&-16&,&25&,&-36&,&49&,&-64\\\\ (3)^2&,&-(4)^2&,&(5)^2&,&-(6)^2&,&(7)^2&,&-(8)^2 \end{array} \\\\\\ \sum\limits_{k=1}^6\ (-1)^{k+1}(k+2)^2[/tex]

[tex]\bf -------------------------------\\\\ \begin{array}{lllllllllll} 3&,&\frac{3}{2}&,&1&,&\frac{3}{4}&,&\frac{3}{5}\\\\ \frac{3}{1}&,&\frac{3}{2}&,&\frac{3}{3}&,&\frac{3}{4}&,&\frac{3}{5} \end{array}\qquad \sum\limits_{k=1}^5\ \cfrac{3}{k}[/tex]