Finding Sum of Telescoping Series?

📌 CONCEPT: A telescoping series is a series where the majority of the terms cancel out, leaving only a few terms, making it easier to find the sum.

📐 RULE / FORMULA: The sum of a telescoping series can be found by adding the first and last terms of the series, as the middle terms cancel each other out. The sum is given by the formula: S = a + l, where a is the first term and l is the last term.

💡 WORKED EXAMPLE: Consider the series 1 - 2 + 3 - 4 + 5 - 6 + ... up to n terms. The first term (a) is 1 and the last term (l) is n. The sum of the series is S = 1 + n. The sum of the series is dependent on n, and the exact expression is 1 + n.

⚠️ COMMON MISTAKE: Students often forget to identify the first and last terms of the series, or they may not cancel out the middle terms correctly, leading to incorrect sums.