Ta có:
$a_{2}$² = $a_{1}$ × $a_{3}$ ⇔ $\frac{a_{1}}{a_{2}}$ = $\frac{a_{2}}{a_{3}}$
$a_{3}$² = $a_{2}$ × $a_{4}$ ⇔ $\frac{a_{2}}{a_{3}}$ = $\frac{a_{3}}{a_{4}}$
⇒ $\frac{a_{1}}{a_{2}}$ = $\frac{a_{2}}{a_{3}}$ = $\frac{a_{3}}{a_{4}}$
⇔ $\frac{a_{1}³}{a_{2}³}$ = $\frac{a_{2}³}{a_{3}³}$ = $\frac{a_{3}³}{a_{4}³}$
= $\frac{a_{1}³+a_{2}³+a_{3}³}{a_{2}³+a_{3}³+a_{4}³}$ (1)
Ta có tiếp: $\frac{a_{1}³}{a_{2}³}$ = $\frac{a_{1}}{a_{2}}$ × $\frac{a_{1}}{a_{2}}$ × $\frac{a_{1}}{a_{2}}$
= $\frac{a_{1}}{a_{2}}$ × $\frac{a_{2}}{a_{3}}$ × $\frac{a_{3}}{a_{4}}$ = $\frac{a_{1}}{a_{4}}$ (2)
Từ (1)(2) ⇔ $\frac{a_{1}³+a_{2}³+a_{3}³}{a_{2}³+a_{3}³+a_{4}³}$ = $\frac{a_{1}}{a_{4}}$ (đpcm)
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#ctlhn
#human dream never stops
