- #1
n_kelthuzad
- 26
- 0
1 to the power of ∞ =e ?
Let there be function f(x):
f(x)=(b+1)^(b+1)/(b+1!)/[(b^b)/b!]
--an example of f(99): 100^100/100!/(99^99/99!)
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and as b gets larger, f(x) converges to e.
so we have:
lim b→ ∞ (b+1)^(b+1)/(b+1!)/[(b^b)/b!]=e
(b+1)^(b+1)/(b^b)/(b+1)=e
(b+1)^(b+1-1)/(b^b)=e
(b+1)^b/(b^b)=e
[(b+1)/b]^b=e
(1+1/b)^b=e
and substitute lim b→∞:
(1+0)^∞=e
1^∞=e
I am happy to hear any disagreements.
Let there be function f(x):
f(x)=(b+1)^(b+1)/(b+1!)/[(b^b)/b!]
--an example of f(99): 100^100/100!/(99^99/99!)
-------------------------------------------------------------------------
and as b gets larger, f(x) converges to e.
so we have:
lim b→ ∞ (b+1)^(b+1)/(b+1!)/[(b^b)/b!]=e
(b+1)^(b+1)/(b^b)/(b+1)=e
(b+1)^(b+1-1)/(b^b)=e
(b+1)^b/(b^b)=e
[(b+1)/b]^b=e
(1+1/b)^b=e
and substitute lim b→∞:
(1+0)^∞=e
1^∞=e
I am happy to hear any disagreements.