help plz

The maximum possible length is 1.

What is the maximum possible length of the vector resulting from the following linear combination?
$\dfrac{1}{\| \mathbf{v_1} \|} \,\mathbf{v_1} + \dfrac{1}{\|\mathbf{v_2}\|} \,\mathbf{v_2} + \cdots + \dfrac{1}{\| \mathbf{v_n} \|} \,\mathbf{v_n}$

I assume:

A unit vector is a vector of length 1.

The unit vector $\hat{v}$ is defined by $\dfrac{\mathbf{v}}{\| \mathbf{v} \|}$

$\begin{array}{|rcll|} \hline && \dfrac{1}{\| \mathbf{v_1} \|} \,\mathbf{v_1} + \dfrac{1}{\|\mathbf{v_2}\|} \,\mathbf{v_2} + \cdots + \dfrac{1}{\| \mathbf{v_n} \|} \,\mathbf{v_n} \\\\ &=& \hat{v} _1 + \hat{v} _2 + \cdots + \hat{v} _n \\ \hline \end{array}$

 The maximum possible length of the vector resulting from the linear combination is
$1+1+ \cdots + 1 = n$