Question

Calculați raportul numerelor a și b dacă: a = 1/1×2 + 1/2×3 + 1/3×4 +...+ 1/42×43 și b = 1/2×3 + 1/3×4 + 1/4×5 +...+ 1/125×126

Answer 1

Răspuns:

Explicație pas cu pas:

$a=...=\dfrac{1}{1}- \dfrac{1}{2}+\dfrac{1}{2}- \dfrac{1}{3}+\dfrac{1}{3}- \dfrac{1}{4}+...+\dfrac{1}{42}- \dfrac{1}{43}=\dfrac{1}{1}- \dfrac{1}{43}=\dfrac{43-1}{43}=\dfrac{42}{43}.\\b=...=\dfrac{1}{2}- \dfrac{1}{3}+\dfrac{1}{3}- \dfrac{1}{4}+\dfrac{1}{4}- \dfrac{1}{5}...+\dfrac{1}{125}- \dfrac{1}{126}=\dfrac{1}{2}- \dfrac{1}{126}=\dfrac{63-1}{126}=\dfrac{62}{126}=\dfrac{31}{63} .\\\dfrac{a}{b}=a:b=\dfrac{42}{43}: \dfrac{31}{63}=\dfrac{42}{43}*\dfrac{63}{31}=\dfrac{2646}{1333}.$