Summation of Infinite Series?

📌 CONCEPT: An infinite series is the sum of an infinite number of terms in a sequence, and it can be finite or infinite depending on the sequence's properties.

The given series 1/2 + 1/4 + 1/8 + ... is a geometric series with first term a = 1/2 and common ratio r = 1/2.

📐 RULE / FORMULA: The sum of an infinite geometric series is given by S = a/(1 - r), where a is the first term and r is the common ratio.

💡 WORKED EXAMPLE: Consider the series 1/2 + 1/4 + 1/8 + ... . Here, a = 1/2 and r = 1/2. Using the formula, we get S = (1/2)/(1 - 1/2) = (1/2)/(1/2) = 1.

⚠️ COMMON MISTAKE: Students often forget to check if the common ratio is within the range -1 < r < 1, which is necessary for the series to converge and have a finite sum.