Value of `y=1+(1)/(2)+(1)/(4)+(1)/(8)+...........` is

Sum the series to infinity : 1 +(1)/(2) +(1)/(4) +(1)/(8) + ...

Find the values of (1)/(12!) + (1)/(10! 2!) + (1)/(8!4!) + …+ (1)/(12!)

Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))........oo is equal to a. 3 b. 6/5 c. 3/2 d. none of these

If y(x) is solution of x(dy)/(dx)+2y=x^(2), y(1)=1 then value of y(1/2)= (a) -(49)/(16) (b) (49)/(16) (c) (45)/(8) (d) -(45)/(8)

If y=(1+x)(1+x^2)(1+x^4)(1+x^8).........(1+x^(2n)) , find (dy)/(dx) .

The value of 2xx2^(1//2)xx2^(1//4)xx2^(1//8)xx ….xx oo is (i) 4 (ii) sqrt(2) (iii) 2sqrt(2) (iv) 8

Prove that: 2^(1/4).4^(1/8), 8^(1/16). 16^(1/32)......... oo=2 .

If x,y in R^(+) such that x + y = 8, then find the minimum value of (1 + (1)/(x)) (1 + (1)/(y))

If 2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(8z)=4 find the value of x.

The line y=mx+1 touches the curves y=-x^(4)+2x^(2)+x at two points P(x_(1),y_(1)) and Q(x_(2),y_(2)) . The value of x_(1)^(2)+x_(2)^(2)+y_(1)^(2)+y_(2)^(2) is