質問: if (1-x+x^2)^n=a0+a1x+a2x^2+....a(2n)x^(2n) then a0+a2+a4+...+a(2n)=
回答: dear manan (1-x+x^2)^n=a0+a1x+a2x^2+....a(2n)x^(2n) put x=1 1 = a0 +a1 +a2 +a3 +a4 + .....a2n .........(1) now put x=-1 3 n = a0 -a1 +a2 -a3 + .....a2n .............(2) add (1) and (2) 3 n +1 = 2[a0 +a2+a4 + ....+a2n] so a0 +a2+a4 + ....+a2n = 1/2 [ 3 n +1] please feel free to post as many doubts on our discussion forum as you can. if you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. we are all iitians and here to help you in your iit jee preparation. all the best. regards, askiitians experts badiuddin