show that the sum of odd coefficients in the expansion (1+2x-3x​2)1025 is an even integer

Dear student
We know thatSum of coefficients of odd terms=f(1)+f(-1)2Let f(x)=1+2x-3x21025So, f(1)=1+2(1)-3(1)21025=1+2-31025=0and f(-1)=1+2(-1)-3(-1)21025=1-2-31025=-41025So, Sum of coefficients of odd terms=f(1)+f(-1)2=0+-410252=-410252 which is an even integer
Regards

  • 5
its difficult question sorry!!
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