Question

How is sum of all natural no.s upto infinty equal to -1/12.​

Answer 1

Step-by-step explanation:

take the following steps:

I start with a series,

A, which is equal to 1–1+1–1+1–1

I’ll write it as such:

A = 1–1+1–1+1–1⋯

Then I do a neat little trick. I take away A from 1

1-A=1-(1–1+1–1+1–1⋯)

1-A=1–1+1–1+1–1+1⋯

1-A =A

1 = 2A

1/2 = A

now,let the b be following

B =1–2+3–4+5–6⋯.

Mathematically, we get this:

A-B = (1–1+1–1+1–1⋯)- (1–2+3–4+5–6⋯)

A-B = (1–1+1–1+1–1⋯) — 1+2–3+4–5+6⋯

Then we shuffle the terms around a little bit, and we see another interesting

pattern emerge.

A-B = (1–1) + (–1+2) +(1–3) + (–1+4) + (1–5) + (–1+6)⋯

A-B = 0+1–2+3–4+5⋯

A-B = B

A = 2B

1/2 = 2B

1/4 = B

let C = 1+2+3+4+5+6⋯

B-C = (1–2+3–4+5–6⋯)-(1+2+3+4+5+6⋯)

B-C = (1-2+3-4+5-6⋯)-1-2-3-4-5-6⋯

B-C = (1-1) + (-2-2) + (3-3) + (-4-4) + (5-5) + (-6-6) ⋯

B-C = 0-4+0-8+0-12⋯

B-C = -4-8-12⋯

B-C = -4(1+2+3)⋯

B-C = -4C

B = -3C

1/4 = -3C

1/-12 = C or C = -1/12

this was proposed by ramanujan a Indian hence jai hind....^_^^_^

hope this helps

mark as brainliest!