Let `S_1 , S_2,`,,,, be squares such that for each `n ge 1` the length of a side of `S_n` equals the length of a diagonal of `S_(n +1)`. If the length of a sides of `S_1` is 10 cm, then for which of the following values of n in the ares of `S_n` less than 1 sq. cm ?

Let S_(n) be the sum of first n terms of an A.P. If S_(2n) = 5s_(n) , then find the value of S_(3n) : S_(2n) .

If S_n be the sum of the n consecutive terms of an A.P,find the value of S_(n+3)-3S_(n+2)+3S_(n+1)-Sn

Which of the following reactions do not invole an intermediate and why? S_(N)1,S_(N)2,EI,E2

Let ABCD is a unit square and each side of the square is divided in the ratio alpha : (1-alpha) (0 lt alpha lt 1) . These points are connected to obtain another square. The sides of new square are divided in the ratio alpha : (1-alpha) and points are joined to obtain another square. The process is continued idefinitely. Let a_(n) denote the length of side and A_(n) the area of the n^(th) square The value of alpha for which side of n^(th) square equal to the diagonal of (n+1)^(th) square is

If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

A rectangle with sides 2m-1 and 2n-1 divided into squares of unit length the number of rectangles which can be formed with sides of odd length is

If S denotes the sum to infinity and S_n the sum of n terms of the series 1+1/2+1/4+1/8+ , such that S-S_n<1/(1000), then the least value of n is 8 b. 9 c. 10 d. 11

If s(n)= i^n+i^(-n) where i=sqrt(-1) and n is an integer then the total number of distinct values of S(n) is

If alpha_1 and alpha_2 be the circular measure of the angles subtended by the arcs of lengths s_1,s_2 at the centres of the circles whose radii are a_1,a_2 respectively , then show that the angle subtended at the centre by the arc of length (s_1+s_2) of a circle whose radius is 1/n(a_1alpha_1+a_2alpha_2) will be n radians.

If alphaa n dbeta are the roots of ax^2+bx+c=0a n dS_n=alpha^n+beta^n, then a S_(n+1)+b S_n+c S_(n-1)=0 and hence find S_5dot