What is the sum of the coefficients of odd powers of x in the expansion of Oneplus x to the power 50?

What is the sum of the coefficients of odd powers of x in the expansion of Oneplus x to the power 50?

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Formula used:

(1 + x) = [nCnC1 x + nC2 x+ … +nCn xn]

  • C0 + C1 + C2 + … + Cn = 2n
  • C0 + C2 + C4 + … =  2n-1
  • C1 + C3 + C5 + … = 2n-1

Calculation:

(1 + x)50  = [50C+ 50C1 x + 50C2 x+ … +50Cn x50]    ----(1)

Here, n = 50

Using the above formula, the sum of odd terms of the coefficient is

S = (50C1 + 50C3­ + 50C5 + ……. + 50C49)

⇒ S = 250-1 = 249

∴ Sum of odd terms of the coefficient = 249

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