A telescoping sum is a sum that is calculated when immediate terms cancel out. For terms like $\frac{1}{n(n + k)}$, it equals $\frac{1}{k}(\frac{1}{n} – \frac{1}{n + 1})$. A special case, 1, must be noted. Everything simplifies to $\frac{1}{n} – \frac{1}{n – 1}$ There are also other telescoping formulas, like General Linear Denominator and Radical Telescoping […]
Tag: AMC
Reducution Efficiency
When you see a large fraction, always reduce with the largest factor first. For example, What is the value of this expression in decimal form? Obviously, this is divisible by 2, but we can do better than that. Did you notice that all of them are divisible by 11? If we reduced by 2, we […]
Always Read the Question!
Always read the question! For example: Find the ones digit of 222222-22222-2222-222-22-2. If you don’t read the question first, you might just calculate the whole thing. But if you did, you could just look at the ones digits. It saves a lot of time.