Question

a)
$\frac{2}{1 \times 3} + \frac{2}{3 \times 5} + .... + \frac{2}{2013 \times 2015}$
b)
$\frac{1}{2 \times 4} + \frac{1}{4 \times 6} + ..... + \frac{1}{2n(2n + 2)} unde \: n \: apartime \: nr \: naturale \: nenule$

Answer 1

2*(1/2)(1-1/3+1/3-1/5+...+1/2013-1/2015)=1-1/2015=2014/2015

1/4 (1/1*2+1/2*3+1/3*4+...+1/n(n+1)) =(1/4)* (1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1))=

1/4 *(1-1/(n+1))=n/4(n+1)