25^(x-1)=5^(2x-1)-100

If 5^(2x-1)-(25)^(x-1)=2500 then find x

prove that int_0^(102)(x-1)(x-2)..(x-100)xx1/(1/(x-1)+1/(x-2)+. .1/(x-100))dx=101 !-100 !

Prove that int_0^(102)(x-1)(x-2)(x-100) x(1/((x-1)+1/((x-2))+1/((x-100))dx=101 !-100 !

Prove that int_0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2) +.... .+ 1/(x-100))dx=101 !-100 !

Prove that int_0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2) +.... .+ 1/(x-100))dx=101 !-100 !

{:("Column" A ,, "Column" B), (225x^(2) - 625 y^(2) = ,, (a) 25(x-2) (x-2)), (x^(2) - x - y - y^(2) = ,, (b) 25(3x- 5y) (3x + 5y)), (x^(2) - x - y^(2) + y = ,, (x + y) (x - y- 1)), (25x^(2) - 100 x + 100 = ,, (d) (x - y) (x + y -1)), (,,(e) (x + y) (x + y - 1)):}

(x-1)/(x^(2)+5x)-(x+1)/(x^(2)-25)

int_(0)^(102)(x-1)(x-2)dots(x-100)xx((1)/(x-1)+(1)/(x-2)+.(.1)/(x-100))dx=101!-100

If the number of terms in the expansion of (1+x)^(101)(1+x^(2)-x)^(100) is n, then the value of (n)/(25) is euqal to

If the number of terms in the expansion of (1+x)^(101)(1+x^(2)-x)^(100) is n, then the value of (n)/(25) is euqal to