Step 1: Identify the type — polynomial sum (use standard formulas), rational sum (partial fractions + telescope), factorial sum (k*k! identity), or irrational sum (rationalize). Step 2: For polynomial sums, expand and apply formulas. Step 3: For telescoping, write out first 3 and last 3 terms to verify cancellation pattern. Step 4: For numerical value questions, compute carefully — arithmetic errors are common. Step 5: Check with small cases (n=1, n=2) to verify your formula. Common mistakes: wrong formula for sum($k^2$), forgetting to subtract when computing sum from m to n (use sum(1 to n) - sum(1 to m-1)), and sign errors in partial fractions. These problems take 2-3 minutes when the technique is recognized.