Question 33 of 58intermediate💡 UnderstandShort Answer2 marks

What does it mean to add an infinite number of terms?

Correct Answer

Adding an infinite number of terms means finding the value that we get “closer” and “closer” to as we add more and more terms of the infinite sum, starting from the first term.

While we can easily add a finite number of terms like 2, 100, or a lakh, an infinite sum cannot be calculated by simply adding forever. Instead, it represents the target value that the partial sums gradually approach.

For instance, in the infinite series for π\pi, 4×(1−1/3+1/5−1/7+…)4 \times (1 - 1/3 + 1/5 - 1/7 + \ldots), adding the infinite terms means finding the value that the sum progressively gets closer to as more terms are included. We will learn more about infinite series in higher grades.

Exercise: 3.5.3 The Story of Pi ($\pi$) and Madhava’s Infinite Series | Q: 1 | (Page 17)
For More Understanding

Explanation

The textbook context directly defines what it means to add an infinite number of terms. It clarifies that unlike adding a finite number of terms (like 2 or 100), adding an infinite number of terms is about finding the value that the sum approaches or gets 'closer and closer' to as more terms are added from the beginning. This concept is introduced in the context of the infinite series for pi.

Solution Steps

  1. Step 1: Identify the textbook definition of adding an infinite number of terms.

  2. Step 2: Explain that it means finding the value we get 'closer' and 'closer' to as we add more and more terms of the infinite sum, starting from the first term.

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