Suppose `p(x)=a_0+a_1x+a_2x^2++a_n x^ndot` If `|p(x)|lt=e^(x-1)-1|` for all `xgeq0,` prove that `|a_1+2a_2++n a_n|lt=1.`

If cosx=a_0+a_1 x+a_2x^2+... then the value of a_2 is

If (1+x)^n=a_0+a_1x+a_2x^2+...+a_nx^n then find : a_1-a_3+a_5-a_7+… .

If (1+x)^n=a_0+a_1x+a_2x^2+...+a_nx^n then find : a_0+a_3+a_6+a_9+… .

If (1+x)^n=a_0+a_1x+a_2x^2).....+a_nx^n then value of the series a_(0)-a_(2) + a_(4)-a_(6) +….. is

If P(x) = a _0 + a _1 x ^(2) + a _2 x^(4) + … + a _n x ^(2n) is a polynomial in a real variable x with 0 lt a _0 lt a _1 lt a _2 lt … lt a_n . Then, the function P (x) has

If (1+x)^n=a_0+a_1x+a_2x^2).....+a_nx^n The sum of the series a_(0) +a_(4) +a_(8)+a_(12)+ …… is