Newton is tired now!

Algebra Level 4

If \(a + b + c + d + e = 1\)

\(a^2 + b^2 + c^2 + d^2 + e^2 = 1\)

\(a^3 + b^3 + c^3 + d^3 + e^3 = 2\)

\(a^4 + b^4 + c^4 + d^4 + e^4 = 3\)

\(a^5 + b^5 + c^5 + d^5 + e^5 = 5\)

then find the value of \(30(a^7 + b^7 + c^7 + d^7 + e^7)\)

This problem is inspired by many problems

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