Square Triangular Number - Numerical Data

Numerical Data

As k becomes larger, the ratio tk / sk approaches and the ratio of successive square triangular numbers approaches .

 \begin{array}{rrrrll}
k & N_k & s_k & t_k & t_k/s_k & N_k/N_{k-1} \\
0 & 0 & 0 & 0 & & \\
1 & 1 & 1 & 1 & 1 & \\
2 & 36 & 6 & 8 & 1.33333 & 36\\
3 & 1\,225 & 35 & 49 & 1.4 & 34.02778\\
4 & 41\,616 & 204 & 288 & 1.41176 & 33.97224\\
5 & 1\,413\,721 & 1\,189 & 1\,681 & 1.41379 & 33.97061\\
6 & 48\,024\,900 & 6\,930 & 9\,800 & 1.41414 & 33.97056\\
7 & 1\,631\,432\,881 & 40\,391 & 57\,121 & 1.41420 & 33.97056\\
\end{array}

Read more about this topic:  Square Triangular Number

Famous quotes containing the words numerical and/or data:

    The terrible tabulation of the French statists brings every piece of whim and humor to be reducible also to exact numerical ratios. If one man in twenty thousand, or in thirty thousand, eats shoes, or marries his grandmother, then, in every twenty thousand, or thirty thousand, is found one man who eats shoes, or marries his grandmother.
    Ralph Waldo Emerson (1803–1882)

    Mental health data from the 1950’s on middle-aged women showed them to be a particularly distressed group, vulnerable to depression and feelings of uselessness. This isn’t surprising. If society tells you that your main role is to be attractive to men and you are getting crow’s feet, and to be a mother to children and yours are leaving home, no wonder you are distressed.
    Grace Baruch (20th century)