Prove (lim n -> infinity) (1 + 1/n)^n = e • Physics Forums
Jan 13, 2005 · The limit of the expression (1 + 1/n)^n as n approaches infinity is proven to equal the mathematical constant e. This proof utilizes L'Hôpital's rule and the properties of …
Proving the Convergence of the Sequence n^(1/n) - Physics Forums
Mar 19, 2010 · The limit of the sequence \ ( n^ {1/n} \) as \ ( n \) approaches infinity is proven to converge to 1. The discussion highlights various methods for proving this limit, including using …
Proving lim (1-1/n)^n=1/e as n Approaches Infinity - Physics Forums
Feb 27, 2008 · The limit of the expression (1 - 1/n)^n as n approaches infinity is established to be equal to 1/e. This conclusion is derived using the properties of logarithms and the continuity of …
Limit n approaches infinity of (1 + n)^(1/n) - Physics Forums
Apr 9, 2013 · 1. lim (1 + n)^(1/n) n→∞ 2. I was able to figure out that the limit goes to 1 only after I substituted larger and larger values in place of n in my calculator. Since I cannot use a …
Convergence of series log (1-1/n^2) - Physics Forums
Sep 14, 2018 · The sum of the series ∑ (n=2 to ∞) ln (1 - 1/n²) converges to -ln (2). This conclusion is reached by recognizing the series as a telescoping series, which can be …
Understanding the Limit of (1+1/n)^n as n Goes to Infinity
Oct 9, 2008 · The limit of (1 + 1/n)^n as n approaches infinity converges to the mathematical constant e, not 1, as commonly misunderstood. The discussion clarifies that while 1/n …
Why (1+1/n)^n goes to e as n goes to infinite? - Physics Forums
Dec 14, 2011 · I uploaded a picture of my question. I am just wondering how to justify how (1 + 1/n)^n goes to e as n goes to ∞? How do you show this? Thanks!
Is sequence 1/ (n-1) necessarily bounded? • Physics Forums
Oct 11, 2014 · Courant states that a convergent sequence is necessarily bounded; that is, for all n, the absolute value of term a n is less than or equal to some number M. My question is does …
Expanding the Exponential Function Using Limits - Physics Forums
Oct 22, 2009 · Is there someone who can explain why this is true, or point me to an online resource that provides a proof of it? e^x = \\lim_{n\\to \\infty} \\left(1 + x/n \\right) ^n I know that …
Prove that n.1 + (n-1).2 + (n-2).33. (n-2) + 2. (n-1) + 1.n = n (n+1 ...
Jul 17, 2011 · The discussion centers on proving the equation n.1 + (n-1).2 + (n-2).3 + ... + 2. (n-1) + 1.n = n (n+1) (n+2)/6. Participants clarify that substituting n=1 into both sides of the …