(1-1/2) (1-1/4) (1-1/8) ... (1-1/2^n) ...
2006-10-04 20:12:10 · 7 answers · asked by Payam Samidoost 2 in Science & Mathematics ➔ Mathematics
what is the limit?
Is it rational or not?
2006-10-04 20:25:46 · update #1
The answer is 1. 2^n...n will go to infinity...that means 2 to the power of infinity is infinity...so 1/infinity is zero..cause anything over infinity is zer0......so 1- zero...will always equal 1 !
2006-10-12 10:02:03 · answer #1 · answered by nor2006 3 · 0⤊ 0⤋
2
2006-10-11 21:22:41 · answer #2 · answered by Mark Antony 3 · 0⤊ 1⤋
limit can't be zero as it will turn the whole product to zero , well it will be infinity
(1-1/2^n) if n=0 then 2^0 will be 1
and it will end in zero and whole product series will end up in zero
and if n=infinity then 2^infinity
will make last term as 1 which will not affect the value of series
well it will be rational series
2006-10-13 01:36:03 · answer #3 · answered by Nick 3 · 0⤊ 1⤋
The limit is zero. As n gets bigger and bigger the factor (1-1/2^n) gets smaller and smaller. The product approaches zero (on the positive side) but never gets there.
Because all of your factors are rational numbers (because they are the difference between two rational numbers) all the numbers in the series are positive.
2006-10-11 15:16:21 · answer #4 · answered by Marcella S 5 · 1⤊ 1⤋
what do you want?
do you want what this is equal to??
see the best way to work this out is to think that the latter terms in the product will be one so not to bother about them, so the product can be roughly approximated by considering on first 5-6 terms in the product.
2006-10-05 05:44:36 · answer #5 · answered by paranoid1288 2 · 1⤊ 0⤋
Looks convergent, but I don't feel like working it, the answer is probably rational.
2006-10-05 06:14:41 · answer #6 · answered by yasiru89 6 · 0⤊ 0⤋
SAHI HAI
2006-10-05 03:20:54 · answer #7 · answered by Ekant 2 · 0⤊ 1⤋