Question

1+2+3+4+5+6+7+8+9++10+__________________________________infinity = Sum of all natural number

Answer 1

yes,because all the counting numbers starting from 1 to endless mode are called natural numbers.
In the above equation,the no. are starting from 1 and are going on till infinity (endless).These all no. are natural numbers.Thus,sum of these no. is equal to sum of all natural no.(which are also infinite or endless)

Answer 2

Answer:

-1/12 .

Step-by-step explanation:

yeah, I knew it looks crazy but it is a well known stabilized result.

I WILL EXPLAIN IT TO YOU IN MOST COMMOM WAY .

Let, 1+2+3+4+5+---= c

1 − 2 + 3 − 4 + ⋯ is the formal power series expansion of the function  

1 / (1 + x)^2  , but with x defined as 1. so we will first turn (1+2+3+4+5---  to 1-2+3-4+5----)

 c = 1 + 2 + 3 + 4 + 5 + 6 ----      

4c =      4       + 8        +12--------

now substract them..

c - 4c = 1 - 2 + 3 - 4 + 5 - 6 + 7 ------

so, now 1 - 2 + 3 - 4 + 5 - 6 + 7 ------ = 1/(1+x)^2 = 1/4

-3c = 1/4   which is equal to -1/12  ...

hence proved !!!

Srinivasa Ramanujan proved it in his notebook chapter 8. Here's a look!