- #1
sponsoredwalk
- 531
- 5
\begin{bmatrix}<br />
1 & \frac{1}{2} & \frac{1}{3} \ldots & \ldots & \frac{1}{n}\\<br />
<br />
\frac{1}{2} & \frac{1}{3} & \frac{1}{4} \ldots & \ldots & \frac{1}{n + 1}\\<br />
<br />
\frac{1}{3} & \frac{1}{4} & \right \frac{1}{5}\ldots & \ldots & \frac{1}{n + 2}\\<br />
<br />
\vdots & \vdots & \vdots & \ddots & \vdots\\<br />
<br />
\frac{1}{n} & \frac{1}{n + 1} & \frac{1}{n + 2} & \ldots & \frac{1}{2n - 1}<br />
<br />
\end{bmatrix}
Express the individual entries h_i_jin terms of i & j.
The answer is
h_i_j = \frac{1}{i + j - 1}
but I can't for the life of me understand how you would recognize that this formula fits the pattern formed in the matrix.
If you were answering this question, would you just attempt to form a formula with n's, i's and j's floating around or is there some method that would be helpful when addressing these types of problems?
Express the individual entries h_i_jin terms of i & j.
The answer is
h_i_j = \frac{1}{i + j - 1}
but I can't for the life of me understand how you would recognize that this formula fits the pattern formed in the matrix.
If you were answering this question, would you just attempt to form a formula with n's, i's and j's floating around or is there some method that would be helpful when addressing these types of problems?
