Answer
$903$ poles.
Work Step by Step
There are $41$ poles in the second row, $40$ poles in the third row, and so on, ending with $1$ pole in the top row.
To go from 42 poles in the bottom layer to one pole in the top layer, where each layer has 1 pole less than the layer below it, there must be 42 layers.
Thus:
${{a}_{42}}=1$ and the number of terms is $n=42$.
The sum of $n\text{th}$term of the arithmetic series is given by:
${{s}_{n}}=\frac{n}{2}\left( {{a}_{1}}+{{a}_{n}} \right)$
Where, ${{a}_{1}}=$first term and ${{a}_{n}}=$$n\text{th}$ term or last term
Substitute the value of ${{a}_{1}}=42$, ${{a}_{n}}=1$ and $n=42$ in the equation ${{s}_{n}}=\frac{n}{2}\left( {{a}_{1}}+{{a}_{n}} \right)$
$\begin{align}
& {{s}_{n}}=\frac{n}{2}\left( {{a}_{1}}+{{a}_{n}} \right) \\
& {{s}_{42}}=\frac{42}{2}\left( 42+1 \right) \\
& =21\times 43 \\
& =903
\end{align}$
Thus, the number of poles in the stack is $903$ poles.
