If (3 x -1) 7 = a 7 x 7 + a 6 x 6 + a 5 x 5 +…. a 1 x + a 0 , then a 7 + a 6 + a 5 +….+ a 1 + a 0 =

Question

If (3 x -1) 7 = a 7 x 7 + a 6 x 6 + a 5 x 5 +&#x2026;. a 1 x + a 0 , then a 7 + a 6 + a 5 +&#x2026;.+ a 1 + a 0 =

Philoid · Accepted Answer

We have,

(3x – 1)⁷ = a₇x⁷+a₆x⁶+a₅x⁵+….a₁x+a₀

Putting x = 1, we get

(3 * 1 – 1)⁷ = a₇ + a₆ + a₅ + a₄ + a₃ + a₂ + a₁ + a₀

(2)⁷ = a₇ + a₆ + a₅ + a₄ + a₃ + a₂ + a₁ + a₀

a₇+a₆+a₅+….+a₁+a₀ = 128