natural

  1. R

    Natural Logarithms with limits

    Hi, I am a bit confused about how to solve this equation below Limit x-->2 ln(x-1) _______ x-2
  2. I

    Equation with natural variable

    \lfloor n/1 \rfloor + \lfloor n/2 \rfloor +...+\lfloor n/(n-1) \rfloor =7\; , n-natural . To write it better : \sum_{j=1}^{n-1} \displaystyle \lfloor \frac{n}{j} \displaystyle \rfloor =7 \; ; n=? , Method Required !
  3. M

    For what natural n is the number (5^(2*n+1))*(2^(n+2))+(3^(n+2))+(2^(2*n+1)) divisibl

    For what natural n is the number (5^(2*n+1))*(2^(n+2))+(3^(n+2))+(2^(2*n+1)) divisible by 19? I get that (19*(50^n + 12^n) + (50-19)(50^n +....+19^n). So it means that n can be any natural number? Or I did some mistake there?
  4. A

    Proof for natural logarithm limit without differentiation

    I have another limit where I'm struggling with the solving.Can somone help me? https://ibb.co/5Kq58jR I used a method like this but I'm not 100% if it's correct! https://ibb.co/JQrpdL1 What should I do from that step? I know something like arctan(x)/x when x tends to 0 is 1. How is that...
  5. A

    Prove the limit of natural logarithm without differentiation or Taylor series

    Can someone help me to prove that this limit is equal to 1 without using differentiation or Taylor Series?(like in the limit of sinx/x when x tends to 0)What are the steps? https://imgur.com/a/WslKnLI
  6. Z

    Limit of a Natural Number Series

    Limit of a Natural Number Series Take a line marked off in unit intervals: 0,1,2,..... Pick a point in (0,1) Divide [0,1] in ten intervals and say p is in fifth interval. Write .4 and mark 4 on the line. Divide fifth interval in 10 again and say p is in seventh sub interval. Write...
  7. L

    Two natural numbers written on the board

    Let us denote two natural number as a and b. Now we have: A=201620162016201620162016=a \cdot \sum_{i=1}^{m}b_{i} and B=201720172017201720172017=b \cdot \sum_{i=1}^{n}a_{i}, where a=\overline{a_{n}a_{n-1}...a_{2}a_{1}} and b=\overline{b_{m}b_{m-1}...b_{2}b_{1}}. Now, we have: A=2016...
  8. G

    What is the average of all the odd natural numbers upto 51?

    Find the the average of all the odd natural numbers upto 51. Sum of odd numbers is n^2. Here n is 51. 51 stands in 26th position in odd natural numbers. Average is \frac{n^2}{26} = 100.03 But answer is 26. Please help me.
  9. Z

    Natural, Rational, and Real, Numbers

    Natural, Rational, and Real, Numbers m/n stands for mth of n, not division. Natural Numbers: 1,2,3,4,.........,n Rational Numbers: 1/n, 2/n, 3/n,.....n/n Real Numbers: n → ∞, (0,1] Or, you could start the natural numbers with zero: Natural Numbers: 0,1,2,3,.........,n-1 Rational...
  10. I

    Natural set

    Show that (5n)! \; \vdots \; 40^n n! \; \; ,\, n \in N or \frac{(5n)!}{40^n n!} \in N If can't post proof, maybe we can (use induction).
  11. V

    derivatives and natural logarithms

    I don't really understand (b) and (c). Thanks beforehand.
  12. Z

    Is an Infinite Binary Sequence a Natural Number?

    Is an infinite binary sequence, interpreted as coefficients of 2^{n}, a natural number? a_{0}a_{1}a_{2}.....\equiv a_{0}\times 2^{0}+a^{1}\times 2^{1} + a_{2}\times 2^{2}+....., \\ \text{where } a_n \in \{0,1\} \\ \text{Example:} \\ 00100....=0\times2^{0}+0\times2^{1}+1\times...
  13. Z

    Real Numbers and Natural Numbers

    A real number is a pair of natural numbers. The natural numbers are expressed as a unique countably infinite sequence of digits (binary, decimal, octagonal, etc.). For example: ......0000347.125000...... There is no conceptual difference between the left and right of the decimal point...
  14. A

    Selecting a Natural and a Real Uniformly at Random

    First Statement to Prove: Given 1) the axiom of choice, 2) a randomly selected infinite binary sequence $S = s_1, s_2, s_3,$... (created via the theoretical flipping of a coin infinitely many times where H = 1 and T = 0), and 3) a definition of "select an element of an infinite set...
  15. I

    Divisible for natural numbers

    Show that :5^nmod (40^n n!)=0 n\in N
  16. agentredlum

    Writing Natural numbers as the sum of 4 squares

    Greetings MMF members and guests. It is a well known result that every Natural number can be written as the sum of $4$ squares. $3$ squares are not enough. (For example , $7$ cannot be written as the sum of $3$ squares) Euler did work on the problem and then Lagrange provided a proof...
  17. S

    x intercept with cosine and natural log equations

    I've got a math question I'm trying to figure out, but it's been so long since I studied math that it's all a blur now. Any help or guidance would be great. You can probably tell by my username how long ago all this was... :eek: Find the x intercept where y = e^cos x and y = x * ln x
  18. I

    Two Natural Variables Equation

    If p and q \in N find p and q p+q=pq
  19. A

    Divisors of natural number n

    Hello could you help me to solve my task n∈N Prove that there is n which has more than 2017 divisors d that: √n ≤ d < 1,01∗ √n Thank you
  20. P

    six digit natural number

    the number of all $6$ digit natural numbers having exactly $3$ even digits and $3$ odd digits