Question

calculati valoarea sumei. ​

Answer 1

$\displaystyle \sum\limits_{k=1}^{2007}\Big(1-\dfrac{1}{k}\Big) - 1 -\sum\limits_{k=1}^{2007}\dfrac{k-1}{k} = \\ \\ = \sum\limits_{k=1}^{2007}\Big(1-\dfrac{1}{k}-\dfrac{k-1}{k}\Big) - 1 =\sum\limits_{k=1}^{2007}\Big(1-\dfrac{1}{k}-\dfrac{k}{k}+\dfrac{1}{k}\Big) - 1 = \\ \\ = \sum\limits_{k=1}^{2007}(1-1)-1 = \sum\limits_{k=1}^{2007}(0) - 1 =0 -1 = -1$

Answer 2

Răspuns:

Explicație pas cu pas:

s = 1/2 + 2/3 +...+ 2006/2007 -

 1 - 1/2 - 2/3 -...- 2006/2007 =

-1.