Posted November 27, 2012 lim((1-1/x)^x) [x→ ∞] = (1-1/e) How would one derive this limit? 0 Share this post Link to post Share on other sites

0 Posted November 27, 2012 lim((1-1/x)^x) [x→ ∞] = 1 not (1-1/e) 0 Share this post Link to post Share on other sites

0 Posted November 27, 2012 The limit is neither 1 nor 1-1/e. It's 1/e. 0 Share this post Link to post Share on other sites

0 Posted November 27, 2012 Sorry messed up the OP. lim(1-(1-1/x)^x) [x→ ∞] = (1-1/e) or lim((1-1/x)^x) [x→ ∞] = 1/e The main question of how it is derived stlil stands. 0 Share this post Link to post Share on other sites

0 Posted November 28, 2012 lim x->∞ ( 1 - 1 / X )^{X} (can be written also as ) = lim x->∞ e^{( X . log( 1 - 1/X ) )} ( expansion of log ( 1 - 1/X) ) is -1*( 1/x + 1/2x^{2} + 1/3x^{3} ..... so on) put this in equation we get = lim x->∞ e^{( -X *(1/x + 1/2x^2 + 1/3x^3 ..... so on ) )} =lim x->∞ e^{( -1 *(1 + 1/2x + 1/3x^2 ..... so on ) )} applying limit we get answer = e ^{-1} 0 Share this post Link to post Share on other sites

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lim((1-1/x)^x) [x→ ∞] = (1-1/e)

How would one derive this limit?

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