2
votes
1answer
58 views

Finding when the distances to three cities again have different digits

Very confused on this question. How would you solve it, and what would be the answer(s). Recently I was driving down the freeway and spotted the following freeway sign with the distances to three ...
1
vote
1answer
64 views

very simple math question

I have this very simple math question: Each person starts working life on a salary of $5000$ dollars and then benefits form an annual increment of $250$ dollars over $40$ years of his career. My ...
0
votes
0answers
123 views

Gauss' Summation Trick; Applications and Generalizations

I'm going to write an article about the summation trick attributed to Guass and its applications and generalizations. I'm sure you know what is the trick I mean: $1+2+\cdots+100=101+101+\cdots+101$ ...
3
votes
2answers
188 views

Find the number of digits of $2013^{2013}$?

Is is possible to find the number of digits of $2013^{2013}$ without a calculator?
1
vote
6answers
276 views

Solve the equation $x-7=28$ [closed]

The question is $x-7=28$ But I'm not sure if when I subtract do I have to change the signs to negative?
12
votes
1answer
168 views

Request for a proof of the following continued-fraction identity

I have been poring over many texts about continued fractions, but none of them seem to be helping me to prove the following beautiful continued-fraction identity (I am nowhere close): $$ ...
1
vote
2answers
64 views

why $\sum_{k=0}^{\infty}(10^{-2})^k = \frac{1}{1-10^{-2}}$

i was reading a book and suddenly saw this step: $\sum_{k=0}^{\infty}(10^{-2})^k = \frac{1}{1-10^{-2}}$ i am actually not bad at calculation and also i am okay in precalculus, but i am really stuck ...
21
votes
7answers
1k views

Sum of the sum of the sum of the first $n$ natural numbers

I have here another problem of mine, which I couldn't manage to solve. Given that: $$x_n = 1 + 2 + \dots + n \\ y_n = x_1 + x_2 + \dots + x_n \\ z_n = y_1 + y_2 + \dots + y_n $$ Find ...
1
vote
1answer
340 views

Multiplication Table with a frame and picture of equal sum

Is there an $n \times n$ multiplication table such that if you form a border of width $k$ ("the frame") and sum its elements, the total will equal the sum of the remaining elements ("the picture")? ...
0
votes
3answers
362 views

Which is the biggest integer that divides all integers that are the product of three consecutive odd numbers?

I read this problem from a high-school-math-problems-calendar, and I'm solving them in my spare time just for the fun of it (what in math is not about the fun? =) ), but this little one it's been hard ...
2
votes
1answer
286 views

Word problems - Sum of squares & a strange function

These were two of 20 problems I had to do in a test today that I didn't manage to solve. 1) Find the least $k$ such that $1^2 + 2^2 + 3^2 + 4^2 + \dots + k^2$ is a multiple of 200. 2) ...
1
vote
3answers
149 views

Easy marketing problem

I am a bit weak at math, and I am hoping you can help me find the fastest way to solve a problem. (I hope I came to the right place). This maybe sounds ridiculous, but I want to mathematically solve ...