\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{e}\Rightarrow\frac{a^4}{b^4}=\frac{b^4}{c^4}=\frac{c^4}{d^4}=\frac{d^4}{e^4}=\frac{2a^4}{2b^4}=\frac{3b^4}{3c^4}=\frac{4c^4}{4d^4}=\frac{5d^4}{5e^4}\)
Theo TCDTSBN ta có:
\(\frac{2a^4}{2b^4}=\frac{3b^4}{3c^4}=\frac{4c^4}{4d^4}=\frac{5d^4}{5e^4}=\frac{2a^4+3b^4+4c^4+5d^4}{2b^4+3c^4+4d^4+5e^4}\left(1\right)\)
Lại có: \(\frac{a^4}{b^4}=\frac{a}{b}\cdot\frac{a}{b}\cdot\frac{a}{b}\cdot\frac{a}{b}=\frac{a}{b}\cdot\frac{b}{c}\cdot\frac{c}{d}\cdot\frac{d}{e}=\frac{a}{e}\left(2\right)\)
từ (1) và (2) => dpdcm