91影视

$\underset{i=i_0}{\overset{l}{鈭�}}\underset{j=j_0}{\overset{m}{鈭�}}\underset{k=k_0}{\overset{n}{鈭�}}{k}^i{j}^k$

$$\begin{gathered} \underset{i=i_0}{\overset{i=l}{鈭�}}\underset{j=j_0}{\overset{j=m}{鈭�}}\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k=\underset{i=i_0}{\overset{i=l}{鈭�}}\left(\underset{j=j_0}{\overset{j=m}{鈭�}}\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k\right) \\ =\underset{i=i_0}{\overset{i=l}{鈭�}}\left(\underset{j=j_0}{\overset{j=m}{鈭�}}\left(\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k\right)\right) \end{gathered}$$

The summation $\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k$can be expanded by replacing k with $k_0$and rewriting each term when k ends at n.

Hence, the number of terms in the summation $\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k$is $k_0-n+1$

Similarly, when expanded $\underset{j=j_0}{\overset{j=m}{鈭�}}\left(\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k\right)$by replacing j from $j_0$to m, the number of $\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k$terms obtained is $j_0-m+1$

Hence, the total number of summands of $\underset{j=j_0}{\overset{j=m}{鈭�}}\left(\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k\right)$is $\left(k_0-n+1\right)脳\left(j_0-m+1\right)$

Similarly, when expanded $\underset{i=i_0}{\overset{i=l}{鈭�}}\left(\underset{j=j_0}{\overset{j=m}{鈭�}}\left(\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k\right)\right)$by replacing i from $i_0$to l, the number of $\underset{j=j_0}{\overset{j=m}{鈭�}}\left(\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k\right)$terms obtained is $i_0-l+1$

The total number of summands in $\underset{i=b_0}{\overset{i=l}{鈭�}}\underset{j=j_0}{\overset{j=m}{鈭�}}\underset{k=k_0}{\overset{k=n}{鈭�}}{k}^i{j}^k$is $\left(i_0-l+1\right)脳\left(k_0-n+1\right)脳\left(j_0-m+1\right)$