Hey here's a real honest question that boggles me on every level. I don't know if anyone can explain it in small, kind words for a sad, ignorant person such as myself. I'm adding the series of reciprocals of n^k. k = 0: 1 - 1 + 1 - 1 + 1 - .... is divergent. k = 1: 1 - 1/2 + 1/3 - 1/4 + 1/5 - ... converges to ln(2). k = 2: 1 - 1/4 + 1/9 - 1/16 + 1/25 - ... converges to pi^2/12. WTF? Why did we go from log to pi? k = 3: 1 - 1/8 + 1/27 - 1/64 + 1/125 - ... converges to 3/4 the Reimann zeta function of 3. QUOOOOOSH that's my brain exploding. But k = 4: 1 - 1/16 + 1/81 + 1/256 + 1/625 + .... converges to 7pi^4/720. Odd, but familiar. And I stopped here as it's late where I am. e, pi, zeta: Why are these seemingly related sequences converging into such vastly different transcendental realms? Is there some progression here? The even powers utilize pi^k (and if k = 0 that can't really affect a divergence) so maybe that's it. How can this be explained elegantly - or, can it?
Hey here's a real honest question that boggles me on every level. I don't know if anyone can explain it in small, kind words for a sad, ignorant person such as myself.
I'm adding the series of reciprocals of n^k.
k = 0: 1 - 1 + 1 - 1 + 1 - .... is divergent.
k = 1: 1 - 1/2 + 1/3 - 1/4 + 1/5 - ... converges to ln(2).
k = 2: 1 - 1/4 + 1/9 - 1/16 + 1/25 - ... converges to pi^2/12. WTF? Why did we go from log to pi?
k = 3: 1 - 1/8 + 1/27 - 1/64 + 1/125 - ... converges to 3/4 the Reimann zeta function of 3. QUOOOOOSH that's my brain exploding.
But k = 4: 1 - 1/16 + 1/81 + 1/256 + 1/625 + .... converges to 7pi^4/720. Odd, but familiar. And I stopped here as it's late where I am.
e, pi, zeta: Why are these seemingly related sequences converging into such vastly different transcendental realms? Is there some progression here? The even powers utilize pi^k (and if k = 0 that can't really affect a divergence) so maybe that's it. How can this be explained elegantly - or, can it?
nice 2nd method is love
Thanks for liking
@@SyberMath love from india
Nice!
Thanks!
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applause!
I appreciate it
I used the first method.
2*3*2=12
Answer = 12
Here in 30 ^ ( 2 x + y) = 2 x 2 x 3 = 12
30 ^ ( 1 - y) = 30 / 3 = 10
Hereby
10 ^ (( 2 x + y) / ( 1 - y))
= 3 0 ^ ( 2 x + y) = 12
Hi
Hello
Take log to the equations, sub them into it and simply it. 😏😏😏😏😏😏
What IF, Calculator is NOT allowed ?
@@nitingl4730I did that in my head, so no calculator isn’t an issue, it’s only basic addition, multiplication and log laws
Second method is a painting
Thank you!
12
why?
12
neden?
12