User:Vishal R shiva/sandbox

Mathematical Evidence for Value Of Sum of Infinity == Author name: R. Big text VISHAL (ISR)

ABSTRACT:- THIS PROPOSAL SHOWS THE MATHEMATICAL EVIDENCE OF VALUE OF SUM OF INFINITY. The ideal guess of S.Ramanujan about the value of sum of infinity is proven by the logical Mathematics by R.Vishal. This shows the evidence and hence confirm the value of infinity. To prove that, we want to consider a square with sides ‘a’ Where a  is side

c is centre

To prove the  value of infinity, “ The difference of the area of any shapes to the square remains some space in which no any definite area of shapes should not be fulfill that space completely and no other shapes cannot be repeated except the Triangle “

Where a = 2r “ r be radius “ Then we want to make the difference of total areas into zero 80	0= a^2-πr^2=(〖2r)〗^2- πr^2 0=(4-π) r^2 The above expressions is considered as EQ ---  Hence its forms spaces at four corners of the square. Shaded portion is acured space.

For one space portion 0/4 = ((4-π)r^2)/4 0 = ((4-π)r^2)/4 In that one portion of free space we can accommodate a triangle

for area of that triangle 1/2 bh=  1/2  ( 3r/4  )   ( 3r/4  )

Substitute 1/2  = Sinθ  Cosθ where  θ=〖45〗^o = Sinθ Cosθ (3r/4)^2--"" Substitute equ "" with Then 0=((4-π)r^2)/4- Sinθ Cosθ (3r/4)^2 For one space 0=[((4-π) r^2)/4- Sinθ Cosθ (3r/4)^2 ]/2 Hence this sequence get infinite more 80 0=[((4-π) r^2)/4- Sinθ Cosθ (3r/4)^2 ]/2--  ∞ Rearrange the above expression ∞= [((4-π) r^2)/4- Sinθ  Cosθ (3r/4)^2 ]/2 For the ∞, ∞=[((4-π) r^2)/4- Sinθ Cosθ (3r/4)^2 ]/2 For the unit value r = 0.5, θ=〖45〗^o Substitute these value then ∞=- 1/120 CONCLUSION:- for above consideration infinite we simply say ∞=  (-1)/12