Question

Efectuati calculele:
1/1*5+1/5*9+1/9*13+...+1/81*85
1/2+1/6+1/12+1/20+1/30+...+1/420
2/8+2/24+2/482/80+2/120+2/168
VA ROG FRUMOS!!! ESTE URGENT!!!

Answer 1

Răspuns:

la prima e facut dincolo

la ultima probabil e 2/4=1/2=1/1*2

Explicație pas cu pas:

vezi atasament

Answer 2

Al treilea:

$\it 2s=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30} +\dfrac{1}{42}=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}=\\ \\ \\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}=1-\dfrac{1}{7}=\dfrac{6}{7}\\ \\ \\ Prin\ \ urmare\ \ 2s=\dfrac{6}{7} \Longrightarrow\ s=\dfrac{3}{7}$