Question

Vă rog frumos!!! E URGENT!!! DAU COROANĂ!!!

Answer 1

$\frac{1}{1 \times 2}+ \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + ... + \frac{1}{2008 \times 2009} =$

$= \frac{2 - 1}{1 \times 2} + \frac{3 - 2}{2 \times 3} + ... + \frac{2009 - 2008}{2008 \times 2009} =$

$= \frac{2}{1 \times 2} - \frac{1}{1 \times 2} + ... - \frac{2008}{2008 \times 2009} =$

$= \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - ... - \frac{1}{2009} =$

$= \frac{1}{1} - \frac{1}{2009} =$

$= \frac{2009}{2009} - \frac{1}{2009} =$

$= \frac{2008}{2009}$

Answer 2

Răspuns:

Explicație pas cu pas:

1/2=1-1/2

1/2×3=1/2-1/3

1/3×4=1/3-1/4

.......................

1/2007×2008=1/2007-1/2008

1/2008×2009=1/2008-1/2009             Le adunam si se vor simplifica termenii ai raman ∑=1-1/2009=2009-1/2009=2008/2009