Question

Calculați : 4/1+2 + 4/1+2+3 + .............. +4/1+2+3+...+50.​

Answer 1

Cu formula lui Gauss, pentru expresiile de la numitor, suma devine:

$\it 8\Big(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\ ...\ \dfrac{1}{50\cdot51}\Big)=8\Big(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\ ...\ +\dfrac{1}{50}-\dfrac{1}{51}\Big)=\\ \\ \\ =8\cdot\Big(\dfrac{1}{2}-\dfrac{1}{51}\Big)=8\cdot\dfrac{49}{51}=\dfrac{392}{51}$