Commander

To Summarize : 1 = 1/1x2 + 1/2x3 + 1/3x4 + ……. + 1/(n-1) x n + 1/n(n+1) + 1/(n+1)(n+2) + 1/(n+2)(n+3) + ………. 1 - (1/1x2 + 1/2x3 + 1/3x4 + ……. + 1/(n-1) x n ) = 1/n(n+1) + 1/(n+1)(n+2) + 1/(n+2)(n+3) + ………. Which is 1/n = 1/n(n+1) + 1/(n+1)(n+2) + 1/(n+2)(n+3) + ………. Therefore 1 = n/n(n+1) + n/(n+1)(n+2) + n/(n+2)(n+3) + ………. OR 1 = 1/(n+1) + n/(n+1)(n+2) + n/(n+2)(n+3) + ………. 13 Sep 2024

We see that while 1 = ½ + 1/2x3 + 1/3x4 + 1/4x5 ……… It also validly sums up for every n terms Ie 1 = ½ + 1/2 for n=2 1 = ½ + 1/2x3 + ⅓ for n=3 1 = ½ + 1/2x3 + 1/3x4 + ¼ for n=4 1 = ½ + 1/2x3 + 1/3x4 + 1/4x5 + ⅕ for n=5 etc OK TY I understood what you said and what you mean ! Thanks ! I can make out many explanations are a bit difficult to understand from the depiction and notes but I can vouch I can explain it more clearly if someone wants to know !

Let’s take a look into the Geometrical Model which has horizontal lines drawn at ½, ⅓, ¼ etc upto infinity The area below each line is same value inn sq units that is ½,⅓,¼, etc Each one of these are also equal to 1/1x2 , 2/2x3, 3/3x4, etc And each has a power expansion of (⅓ + ⅓^2 +⅓^3 …) , (¼ + ¼^2 + ¼^3 ….) . (⅕ + ⅕^2 +⅕^3 ….. ) And now. The area below each line is the sum of all rectangles below it : That is ½ = 1/2x3 + 1/3x4 + 1/4x5 …… ⅓ = 1/3x4 + 1/4x5 + 1/5x6 ……. ¼ = 1/4x5 +1/5x6 + 1/6x7 …….. Etc And therefore the Walker’s Series is proved as 1 = 2/2x3 + 2/3x4 + 2/4x5 …….. 1 = 3/3x4 +3/4x5 + 3/5x6 ……… 1 = 4/4x5 + 4/5x6 + 4/6x7 ……… By Wg Cdr Thomas Walker Bangalore India 11 Sep 24

This is some recognition I got in a paper when I was putting up my findings in some University websites

Walker's Equation by Wg CdrThomas Walker.pdfWgCdrThomasWalkersTheories.pdfWalker's Equation.docWalkerEqn Jim Loy.docACuriousConnection.pdf Now with these basic Structures indicated I believe that Logically , Algebraically and by Mathematical Induction we can expand these equations to explore and detect other Relations involving numbers other than Integers ! BTW Some of these old documents may contain my old Contact details My present address Flat # 003 Sai Excellency Apartments 2nd Cross Hennur main road Bangalore 560043 India Phone 9880184818 and 8884577768 both having WhatsApp

Hi Joigus TY Earlier I had given the proof of Walker’s Equation and now I have depicted the Proof Geometrically as can been seen both for Summing upto 1 and converging The same depiction also indictes the Geometric representation of Walker’s Series for those who can visualise ! The General form of Walker’s Series for n from 1 to infinity can also be inferred from this ! If I write up more on this I will put up here ! We can see 1/n = 1/(n+1) + 1/(n+1)^2 + 1/(n+1)^3 + …… as per Walker’s Equation Proof Steps. Which is : 1/n - 1/n+1 = inverse powers of (n+1) from 2 to infinity as shown above which can be called RHS The LHS is 1/n - 1/n+1 = 1/n(n+1) And this progression goes on …….. The LHS a Linear sum of Factors adds up to 1 and the RHS a double matrix depiction of inverse powers adds up to 1 too ! The LHS gives rise to the Walker’s Series and the RHS gives rge Walker’s Equation ! Hi Yes Harmonic Series is Divergent but Walker’s Series is not divergent. No member of the Series has a value of more than 1/(n+1) and no FACTOR used in the Equation will be less than ‘n’ in value either in Denominator or Numerator. 1 = n/n(n+1) + n/(n+1)()n+2) + n/(n+2)(n+3) + …….. If n = 1 : then 1/1x2 + 1/2x3 + 1/3x4 + ……… As n increases 1= 2/2x3 + 2/3x4 + 2/4x5 + ………. Similarly 1 = 3/3x4 + 3/4x5 + 3/5x6 + ……. 1 = 4/4x5 + 4/5x6 + 4/6x7 + ……….. . . .

Hi Yes Harmonic Series is Divergent but Walker’s Series is not divergent. No member of the Series has a value of more than 1/(n+1) and no FACTOR used in the Equation will be less than ‘n’ in value either in Denominator or Numerator. 1 = n/n(n+1) + n/(n+1)()n+2) + n/(n+2)(n+3) + …….. If n = 1 : then 1/1x2 + 1/2x3 + 1/3x4 + ……… As n increases 1= 2/2x3 + 2/3x4 + 2/4x5 + ………. Similarly 1 = 3/3x4 + 3/4x5 + 3/5x6 + ……. 1 = 4/4x5 + 4/5x6 + 4/6x7 + ……….. . . .

1 = 1/(n+1) + n/(n+1)(n+2) + n/(n+2)(n+3) + n/(n+3)(n+4) …. etc till infinity For any n (positive integer) from 1 to infinity This may be called Walker’s Series’ By Wg Cdr Thomas Walker - 22 Aug 2024 FYI plz

Hi I give here the Geometric Model and representation of Walker's Equation and proposal of an Equation od Infinite Series which I call 'Walker's Series' which appears to have escaped many ! Proof of Walker's equation.docx - Google D Dear Moderator, I tried to remove the duplicate images in this post but couldn't succeed Plz remove the repeating pics TY !

The area is around 0.0913 Pi/6 - (Sqrt 3 /4) Using Pi = 22/7 gets this result !

The strip shown has two sides : A straight line of 1 Unit Length and an arc from a Circle having a radius of 1 Unit ! The diagram is shown below. Find the Area of the Strip in Square Units of the same Unit !

A land owner inherits a Circular Piece of land and shares it with his siblings and children ! He lays out four plots of identical shape having 1/11 (one eleventh) of the total land and four other identical plots each having area of 1/4 Square kilometre each. He retains for himself a Square Plot of 1 Square kilometre ! You are required to show the layout of how he did it specifying the dimensions !

Yes TY all for answers ! Pi/6 is the Fraction and 3xSqr Rt 3 times is the Volume of the Bigger Sphere to that of the Smaller one ! Quite Straight forward !

If *C* is a Cube and *S1* is the Sphere Inscribed and *S2* is the Sphere Superscribed then (1) What is the fraction of the volume of *C* is contained in *S1* (2) How many times the volume of *S2* is that of *S1*

E = M C 2 That is : E >>> Energy | Ego | Eminence M >>> Mind | Mobility | Maturity C >>> Creativity | Conscience | Courage

Need to cut like that !

You need to chop of four corners with an equilateral triangle as the base with sides of diagonals Four of them That leaves a tetrahedron in the middle We need to cut it in four equal parts with each equilateral triangular base (four of them) and apex meeting at the center of the cube The four earlier cut pieces (cut for the sake of explanation) are merged with equal area bases of the four pieces of the tetrahedron

Also all the faces of the pieces must be TRIANGLES ! Sorry I forgot to mention this !

Please note it is four pieces and not six ! Error regretted !!

Cut a Cube into six identical pieces each having nine edges !

Correct

Yes Right well done !

Correct ! Well done !!

Not a wordplay The area of the circle