sum_(|f^(k=0)(x,y))^(200)i^(k)+prod_(p=1)^(50)i^(p)=x+iy

If sum_(k=0)^(200)i^(k)+prod_(p=1)^(50)i^(p)=x+iy then (x,y) is

If sum_(k=0)^(200)i^k+prod_(p=1)^(50)i^p =x+iy then (x,y) is

If omega ne 1 is a cube root of unity, then z=sum_(k=1)^(60)omega^(k) - prod_(k=1)^(30)omega^(k) is equal to

If int _(0)^(1) (sum _(r=1) ^(2013)(x)/(x ^(2)+r ^(2)) prod_(r=1)^(2013)(x ^(2) +r ^(2) )) dx =1/2 [(prod_(r=1)^(2013)(1+r ^(2)))-k^(2)] then k=

If int _(0)^(1) (sum _(r=1) ^(2013)(x)/(x ^(2)+r ^(2)) prod_(r=1)^(2013)(x ^(2) +r ^(2) )) dx =1/2 [(prod_(r=1)^(2013)(1+r ^(2)))-k^(2)] then k=

If f(x)=prod_(n=1)^(100)(x-n)^(n(101-n)), where prod_(i=1)^(k)a_(i) stands for product a_(1)dot a_(2).........a_(k), then (f(101))/(f'(101))=(a)5050( b) (1)/(5050) (c) 10010 (d) (1)/(10010)

The sum and sum of squares corresponding to length x (in cm) and weighty (k. gm) of 50 plant products are given below: sum_(i=1)^(50) x_(i) = 212 , sum_(i=1)^(50) x_(i)^(2)=902.8 , sum_(i=1)^(50) y^(i)=261 , sum_(i=1)^(50) y_(i)^(2)=1457.6 Which is more varying , the length or weight ?

Find coeff. of x^(25) in the expansion of sum_(k=0)^(50)(-1)^(k)""^(50)C_(k)(2x-3)^(50-k)(2-x)^(k) .

Find coeff. of x^(25) in the expansion of sum_(k=0)^(50)(-1)^(k)""^(50)C_(k)(2x-3)^(50-k)(2-x)^(k) .