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.`

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.

Suppose p(x) = a_0 + a_1x + a_2x^2 +…+ a_nx^n . If |p(x)| le |e^(x-1) - 1| le 1 then prove |a1 + 2a2 +...... + n an| ≤ 1.

Let P(x)=a_0+a_1x+a_2x^2+...+a_nx^n.If|P(x)|le|e^(x-1)-1,|AAxge0, then the maximum value of |a_1+2a_2+3a_3+..+na_n|

If |a_1sinx+a_2sin2x++a_nsinn x|lt=|sinx| for x in R , then prove that |a_1+2a_2+3a_3+n a_n|lt=1

If |a_1sinx+a_2sin2x++a_nsinn x|lt=|sinx| for x in R , then prove that |a_1+2a_2+3a_3+n a_n|lt=1

If |a_1sinx+a_2sin2x++a_nsinn x|lt=|sinx| for x in R , then prove that |a_1+2a_1+3a+3+n a_n|lt=1

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_1 +a_2 + ……a_(2n) = 3^n

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_2 +a_4+……+a_(2n) = (3^n +1)/(2)

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_2 +a_4+……+a_(2n) = (3^n +1)/(2)

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 +a_1 +a_2 + ……+a_(2n) = 1