The value of `C (47, 4) + underset (r=1) overset (5) sum (52-r,3)` is:

The value of ""^50C_4+ underset (r=1) overset (6) sum ""^(56-r)C_3 is :

Prove that underset (r=1) overset (5) sum "^5C_r=31 .

Evaluate : underset (r=1) overset (n) sum ""^nC_r 2^r .

Equation x^(n)-1=0,ngt1,ninN, has roots 1,a_(1),a_(2),...,a_(n),. The value of underset(r=2)overset(n)sum(1)/(2-a_(r)), is

Equation x^(n)-1=0,ngt1,ninN, has roots 1,a_(1),a_(2),...,a_(n),. The value of underset(r=2)overset(n)sum(1)/(2-a_(r)), is

The value of cot (underset(n=1)overset(23)sum cot^(-1) (1 + underset(k=1)overset(n)sum 2k)) is

The value of overset5 underset(1)sum(n) is:

If R_(1) is the circumradius of the pedal triangle of a given triangle ABC, and R_(2) is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_(3), R_(4) ..., then the value of underset( i=1)overset(oo)sum R_(i) , where R (circumradius) of DeltaABC is 5 is

If x_1,x_2,………….x_p are p values of variabled x such that underset(i=1)overset(p)sum(x_i-2)=110 and underset(i=1)overset(p)sum(x_i-5)=20 find the value of p and the mean.

Prove that underset (r=0) overset (n) sum 3^r ""^nC_r =4^n .