- A square is inscribed in a circle of radius R, a circle is inscribed in this square, then a square in this circle and so on n times. find the limit of the sum of areas of all the squares as n tends to infinity.
- Let f(x) be a real value of function not identically zero, satisfies the relation f(x+y7) = f(x) +{f(y)}7 for all real x and y and the values of f '(0) is non negative where n(>1) is an odd natural numbers then show that f(1-x)+f(x) =1 .
side of 1st square inscribed will be sqrt2(R)
so area is 2R2
proceeding similarly,by observartion the sides of square's are 21/2R,R,R/21/2,R/2*21/2.....
so sum of areas = 2R2 + R2 + R2/2 + R2/4 + R2/8....
= 2R2 + R2(1 + 1/2 +1/4 +1/8 + ......),
= 4R2
so area is 2R2
proceeding similarly,by observartion the sides of square's are 21/2R,R,R/21/2,R/2*21/2.....
so sum of areas = 2R2 + R2 + R2/2 + R2/4 + R2/8....
= 2R2 + R2(1 + 1/2 +1/4 +1/8 + ......),
= 4R2
side of 1st square inscribed will be sqrt2(R)
so area is 2R2
proceeding similarly,by observartion the sides of square's are 21/2R,R,R/21/2,R/2*21/2.....
so sum of areas = 2R2 + R2 + R2/2 + R2/4 + R2/8....
= 2R2 + R2(1 + 1/2 +1/4 +1/8 + ......),
= 4R2
so area is 2R2
proceeding similarly,by observartion the sides of square's are 21/2R,R,R/21/2,R/2*21/2.....
so sum of areas = 2R2 + R2 + R2/2 + R2/4 + R2/8....
= 2R2 + R2(1 + 1/2 +1/4 +1/8 + ......),
= 4R2