Inductive method is suitable

Correct option is A

S. Ans. (a) for establishing the formula

Solution:
The inductive method is particularly suitable for establishing a formula or a general rule. In this method, we observe specific cases, identify patterns, and then generalize the findings to create a formula or rule. This approach involves reasoning from the specific to the general. For example, in mathematics, the sum of the first $n$ natural numbers can be derived using the inductive method by observing patterns in specific cases and then generalizing to find the formula.

Hence, the correct answer is (a).

Information Booster:

1. The inductive method relies on observation and experimentation to derive general principles.
2. It is widely used in scientific research and mathematical problem-solving.
3. Induction involves reasoning from specific cases to broader generalizations.
4. The method is helpful in exploring new phenomena or uncharted areas.
5. It is essential to verify inductive conclusions through additional methods like deduction.
6. Patterns identified through induction can sometimes lead to exceptions; hence verification is crucial.
7. This method emphasizes observation, classification, and pattern recognition.

Additional Information:

• (a) Establishing the formula: Inductive reasoning is primarily focused on this task by observing patterns in specific cases and generalizing them.
• (b) Solving problems through formula: This task is generally associated with the deductive method, where a formula is applied to solve specific cases.
• (c) Searching for the solution: Problem-solving methods, such as trial-and-error or exploratory approaches, are used instead of strict induction.
• (d) Understanding the solution: Analytical and explanatory methods are better suited for comprehension than the inductive method.

Key Points:

• Inductive methods are exploratory and focus on forming generalizations.
• Deductive methods focus on applying established formulas or rules.
• Both methods complement each other in research and learning.