Question

S= 1+2+3+4+5+6+7-------------​

Answer 1

Answer:

If it is a sum of first n natural numbers, the sum would be

n(n+1)/2

If the sum is up to infinity, the sum is equal to -1/12. thanks to sir Ramanujan.

However, in order to know the proof, we need to know the basic arithmetic assumptions with infinity.

i.e. infinity +_ x = infinity

where x is any number however large.

infinity * x or Infinity ÷ x = infinity

Further we need to know results of two infinite sums in order to understand the proof

1. 1-1+1-1+1-1+1-1+1-1............

let x = 1-1+1-1+......

x = 1 - (1 -1 +1 -1+......). (infinity - 1 = infinity)

x = 1 - x

x + x = 1

2x = 1

x = 1/2

2. 1-2+3-4+5-6+........

let. x = 1-2+3-4+5-6+.......

x =. 1-2+3-4+5-........

------------------------------------

2x = 1-1+1-1+1-1+.........

2x = 1/2. (from previous solution)

x = 1/4

now, our series

x = 1+2+3+4+5+6+.....

1/4 =. 1- 2+3-4+5-6+.... (from previous series)

-. -. +. -. +. -. +

-------------------------------

x - 1/4 = 4. +8. +12. +..

x - 1/4 = 4+8+12+.....

x - 1/4 = 4(1+2+3+......)

x - 1/4 = 4x

4x - x = -1/4

3x = -1/4

x = -1/12

(I don't know what actually your question was, but I enjoyed in reiterating Ramanujan proof)