solve it in Poisson Theorem

[neworld222]

look at the question ,i can't solve it perfactly

 

[tkhunny]

Ponder the limit as x increases without bound

(1 + 1/x)^x

It is 1/e.

Now this one

(1 + 1/(ax))^x

It is e^(-1/a)

I think the idea is that 100 is sufficiently large, though a long way to go for an actual limit, that it is a good enough approximation just to use the limit.

 

[neworld222]

Ponder the limit as x increases without bound

(1 + 1/x)^x

It is 1/e.

Now this one

(1 + 1/(ax))^x

It is e^(-1/a)

I think the idea is that 100 is sufficient large, though a long way to go for an actual limit, that it is a good enough approximation just to use the limit.

yes,you're right.
but i still can't solve it ,that how y go from step2 to step 3.
i get subject on a book.
there says y go from step 2 to setp 3 by 'poisson theorem'.
i don't comprehend about 'poisson theorem'.so i need help in this math forum

 

[tkhunny]

Can't solve what? The second expression IS the limit as x increases without bound. Using the limit as an approximation is all that is happening. Thus the "approximately equal to" symbol.

 

[neworld222]

Can't solve what? The second expression IS the limit as x increases without bound. Using the limit as an approximation is all that is happening. Thus the "approximately equal to" symbol.

thx i had solved it