Question

Să se efectueze calculele :
a.) ( 1/11 + 13/22 + 14/33 + 15/44 + ... + 77/726) - ( 1/2 + 1/3 + 1/4 + ... + 1/66 )
b.) ( 1/7 + 9/14 + 10/21 + ... + 70/441 ) - ( 1/2 + 1/3 + 1/4 + ... + 1/63 )
c.) 8/7 + 9/14 + 10/21 + ... + 70/441 ) - ( 1/2 + 1/3 + 1/4 + ...+ 1/63 )

Vă rog frumos , să-mi spune-ţi cum aţi făcut .

Answer 1

[tex]b)S=( \frac{1}{1 \cdot 7} +\frac{9}{2 \cdot 7}+\frac{10}{3 \cdot 7}+...+\frac{70}{63 \cdot 7})-( \frac{1}{2} +\frac{1}{3}+...+\frac{1}{63})\\ S= \frac{1}{7} \cdot(1+ \frac{9}{2} + \frac{10}{3} +...+ \frac{70}{63} )- (\frac{1}{2} +\frac{1}{3}+...+\frac{1}{63})\\S= \frac{1}{7} \cdot(63+ \frac{7}{2} + \frac{7}{3} +...+ \frac{7}{63}) -(\frac{1}{2} +\frac{1}{3}+...+\frac{1}{63})= \frac{63}{7} =9[/tex]