Question

Hi,
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It's a challenge to all the " moderators , brainly star and maths aryabhatta " title holder .

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$Find. \\ \\ 1 + 2 + 3 + 4 + 5 + 6 + 7 + ...... \infty = ?$
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Answer 1

$1 + 2 + 3 + 4 + 5 + 6..... \infty = ( - \frac{1}{12} )$

Answer 2

Hi friend!!!

Firstly, Consider

1-1+1-1+1-1+.......... =p---(1)

Multiplying '-' on both sides, we get

-(1-1+1-1+1-1+....)=-p

Adding 1 on both sides ,we get

1-(1-1+1-1+1-1+....)=1-p

1-1+1-1+1-1+1......=1-p

From (1) we get

p=1-p

2p=1

p=1/2.

So, 1-1+1-1+1-1+1.....=1/2-----(2)

Now consider,

1-2+3-4+5-6+7-8+.....=q
0+1 -2+3-4+5-6+7-....=q
(+)
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1-1+1-1+1........=2q

From (2)

1/2=2q

1/4=q

So, 1-2+3-4+5-6+....=1/4 ------(3)

Now, the question comes,

1+2+3+4+5+6+........=r ---(4)

Subtracting (3) and (4)

1+2+3+4+5+6......=r
1 -2+3-4+5-6......=1/4
(-)

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4+8+12+16....=r-1/4

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

From (4), we get

4r=r-1/4

3r=-1/4

r=-1/12

So, 1+2+3+4......=-1/12

I hope this will help you ;)