Show-that-the-sum-of-odd-coefficients-in-the-expansion-of-1-2x-3x-2-1025-is-an-even-integer-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 22392 by Tinkutara last updated on 17/Oct/17

Show that the sum of odd coefficients in the expansion of (1 + 2x − 3x^2 )^(1025) is an even integer.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{coefficients} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}\:+\:\mathrm{2}{x}\:−\:\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{1025}} \\ $$$$\mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{integer}. \\ $$

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Show-that-the-sum-of-odd-coefficients-in-the-expansion-of-1-2x-3x-2-1025-is-an-even-integer-

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