(E)/(N!)

The value of lim_(ntooo) (1)/(n)[e^(1/n)+e^(2/n)+...+e] is

The value of lim_(nrarroo)((e^((1)/(n)))/(n^(2))+(2e^((2)/(n)))/(n^(2))+(3e^((3)/(n)))/(n^(2))+…+(2e^(2))/(n)) is

The value of lim_(nrarroo)((e^((1)/(n)))/(n^(2))+(2e^((2)/(n)))/(n^(2))+(3e^((3)/(n)))/(n^(2))+…+(2e^(2))/(n)) is

Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]

A series of concentric ellipse E_1,E_2,E_3,…,E_n is constructed as follows: Ellipse E_n touches the extremities of the major axis of E_(n-1) and have its focii at the extremities of the minor axis of E_(n-1) . If eccentricity of ellipse E_n is e_n , then the locus of (e_(n)^(2),e_(n-1)^(2)) is

If n(H nn E) = 11 , n(H - E) = 22 , n(E - H) = 12 , find n(H) , n(E) and n(H uu E)

A series of concentric ellipses E_1,E_2, E_3..., E_n are drawn such that E touches the extremities of the major axis of E_(n-1) , and the foci of E_n coincide with the extremities of minor axis of E_(n-1) If the eccentricity of the ellipses is independent of n, then the value of the eccentricity, is

A series of concentric ellipses E_1,E_2, E_3..., E_n are drawn such that E touches the extremities of the major axis of E_(n-1) , and the foci of E_n coincide with the extremities of minor axis of E_(n-1) If the eccentricity of the ellipses is independent of n, then the value of the eccentricity, is

lim_ (n rarr oo) {(e ^ (1 / n)) / (n ^ (2)) + (2 * (e ^ (1 / n)) ^ (2)) / (n ^ (2)) + (3 * (e ^ (1 / n)) ^ (3)) / (n ^ (2)) + ... + (n * (e ^ (1 / n)) ^ (n)) / ( n ^ (2))}