Question

Prove that 1+2+3+4+5...........Infinity =-1/12
Ramanujan​

Answer 1

Answer:

IT IS A HYPOTHESIS SO IT CAN NOT BE PROVED........PLZ DO NOT MENTION QUESTIONS WHICH R BASED ON HYPOTHESIS

Answer 2

Step-by-step explanation:

Let S = 1+2+3+4+5+6+7

Consider S1= 1-1+1-1+1-1+1-1…

1-S1=1-(1-1+1-1+1-1+1…)

1-S1=1-1+1-1+1-1+1…..

1-S1=S1

So, S1=1/2

Let S2=1-2+3-4+5-6+7…..

So, S2=1-2+3-4+5-6+7-8+9…..

S2= 1-2+3-4+5-6+7-8……. I have shifted RHS by a unit position

+ 2S2=1-1+1-1+1-1+1…..

Hence, 2S2=S1

Therefore, S2=1/4

Let’s come back to our sum of infinite numbers.

S=1+2+3+4+5+6+7+8+9…..

S2=1-2+3-4+5-6+7-8+9….

So, S-S2=4+8+12+16+20…..

Hence, S-S2=4(1+2+3+4+5+6+7+8….)

S-S2=4S

So, -S2=3S

And, S=-S2/3=-1/12

Hope it helps

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