The sum `sum_(i=0)^m ((10),(i))((20),(m-1))`, where `((p),(q))=0` if `p lt q`, is maximum when m is equal to (A) 5 (B) 10 (C) 15 (D) 20

Find the sum sum_(k=0)^(10)^(20)C_kdot

If f(m) = sum_(i=0)_(m) ({:(30),(30-i):})({:(20),(m-i):}) where ({:(p),(q):})= ""^(p)C_(q) , then

The value of sum_(k=0)^(n)(i^(k)+i^(k+1)) , where i^(2)= -1 , is equal to

Find the sum sum_(i=0)^r.^(n_1)C_(r-i) .^(n_2)C_i .

The value of sum_(n=0)^(100)i^(n!) equals (where i=sqrt(-1))

The value of sum_(n=1)^(13) (i^n+i^(n+1)) , where i =sqrt(-1) equals (A) i (B) i-1 (C) -i (D) 0

("lim")_(n->oo)sum_(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (c) 19 (d) 20

Let P_i and P_i ' be the feet of the perpendiculars drawn from the foci Sa n dS ' on a tangent T_i to an ellipse whose length of semi-major axis is 20. If sum_(i=0)^(10)(S P_i)(S^(prime)P_i ')=2560 , then the value of eccentricity is (a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5

The sum sum_(k=1)^(10)underset(i lt j lt k)underset(j=1)(sum^(10))sum_(i=1)^(10)1 is equal to

The sum sum_(k=1)^(10)underset(i ne j ne k)underset(j=1)(sum^(10))sum_(i=1)^(10)1 is equal to