Question

sᴏʟᴠᴇ ᴛʜɪs !

ᴘrove that 1+2+3+4+5+6+7.......=-1/12​​

Answer 1

Step-by-step explanation:

27×-1/12.............

Answer 2

Step-by-step explanation:

Hello frnd!

Hope this may help you.! :)

The sum of this series is -1/12 . This can be proved by Riemann zeta function.

But ramanujan have proved it by a different method as follows…

Let,

X=1+2+3+4+5+6+… ____(1)

4X= 4 + 8 + 12 +...____(2)

=>-3X=1–2+3–4+5–6+… (subtracting 2 from 1)

=>-3X=1/(1+1)^2 _____by binomial theoram

=>-3X=1/4

=>X=-1/12

Proved.