Evaluate : `sum_(j=1)^10 {(1/2)^(j-1)+(1/5)^(j+1)}`.

Find the value of sum_(r=1)^(10)sum_(s=1)^(10)tan^(-1)(r/s)dot

Let S_(1) = sum_(j=1)^(10) j(j-1).""^(10)C_(j), S_(2) = sum_(j=1)^(10)j.""^(10)C_(j) , and S_(3) = sum_(j=1)^(10) j^(2).""^(10)C_(j) . Statement 1 : S_(3) = 55 xx 2^(9) . Statement 2 : S_(1) = 90 xx 2^(8) and S_(2) = 10 xx 2^(8) .

Evaluate sum_(i=0)^(n)sum_(j=0)^(n) ""^(n)C_(j) *""^(j)C_(i), ile j .

Evaluate sum_(i=0)^(n)sum_(j=0)^(n) ""^(n)C_(j) *""^(j)C_(i), ile j .

S=sum_(i=1)^nsum_(j=1)^isum_(k=1)^j1

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +…+ C_(n) x^(n) , find the values of the following . sum_(i=0)^(n) sum_(j=0)^(n) (i+j) C_(i) C_(j)

The value of expression ^47 C_4+sum_(j=1)^5^(52+j)C_3 is equal to

The value of sum_(i=0)^oosum_(j=0)^oosum_(k=0)^oo1/(3^i3^j3^k) is

The value of the expression ""^(47)C_(4) + sum_(j =1)^(5)""^(52-j)C_(3) is equal to :

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) f(1/3).f(2/3)=1 (C) the value of J equals to 1/2 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J