MathDB

Problem 2

Part of 1998 VJIMC

Problems(2)

e-like limit as n-> infinity

Source: VJIMC 1998 1.2

8/1/2021
Find the limit lim⁡n→∞((1+1n)ne)n.\lim_{n\to\infty}\left(\frac{\left(1+\frac1n\right)^n}e\right)^n.
limitsreal analysis
palindrome in arithmetic sequence exists?

Source: VJIMC 1998 2.2

8/24/2021
Decide whether there is a member in the arithmetic sequence {an}n=1∞\{a_n\}_{n=1}^\infty whose first member is a1=1998a_1=1998 and the common difference d=131d=131 which is a palindrome (palindrome is a number such that its decimal expansion is symmetric, e.g., 77, 3333, 433334433334, 21353122135312 and so on).
arithmetic sequencealgebranumber theorypalindrome