The expression given is:

$\sum_{i=2}^{7} 3^i$

To compute this, we evaluate $3^i$ for each integer $i$ from 2 to 7, and then sum those results.

1. When $i = 2$: $3^2 = 9$
2. When $i = 3$: $3^3 = 27$
3. When $i = 4$: $3^4 = 81$
4. When $i = 5$: $3^5 = 243$
5. When $i = 6$: $3^6 = 729$
6. When $i = 7$: $3^7 = 2187$

Now, summing these values:

$9 + 27 + 81 + 243 + 729 + 2187 = 3276$

Thus, the result of the summation is:

$\sum_{i=2}^{7} 3^i = 3276$

Would you like more details on the calculation process or have any questions?

Here are some related questions to explore further:

1. How would you compute a summation with a different base, such as $5^i$ instead of $3^i$?
2. What is the general formula for the sum of a geometric sequence?
3. How would the result change if the range was $i=1$ to $i=7$ instead?
4. How would you calculate the sum if the exponent was variable, like $3^{i+1}$ instead of $3^i$?
5. What would happen if you used a different lower limit, such as $i=3$?

Tip: In summation problems with exponential terms, identify if it forms a geometric sequence to simplify calculations.