STATEMENT-1 : The sum of reciprocals of first n terms of the series ` 1 + (1)/(3) + (1)/(5) + (1)/(7) + (1)/(9) + … "is" n^(2) ` and
STATEMENT-2 : A sequence is said to be H.P. if the reciprocals of its terms are in A.P.

Options

A. Statemant-1 is True , Statement-2 is True, Statement -2 is a correct explanation for Statement-1
B. Statemant-1 is True , Statement-2 is True, Statement -2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Stetement-2 is False.
D. Statement-1 is False, Statement-2 is True

Answer

To solve the problem, we need to analyze both statements provided and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1:** The sum of reciprocals of the first n terms of the series \( 1 + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{9} + \ldots \) is \( n^2 \).

1. The series given is the sum of the reciprocals of the first n odd numbers.
2. The first n odd numbers are \( 1, 3, 5, 7, \ldots, (2n - 1) \).
3. The reciprocals of these numbers are \( 1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \ldots, \frac{1}{(2n-1)} \).

To find the sum of the reciprocals, we denote it as:
\[ S_n = 1 + \frac{1}{3} + \frac{1}{5} + \ldots + \frac{1}{(2n - 1)} \]

4. It is known from mathematical results that:
\[ S_n = \frac{n^2}{2} \]
However, the statement claims \( S_n = n^2 \), which is incorrect.

### Step 2: Analyze Statement 2
**Statement 2:** A sequence is said to be H.P. if the reciprocals of its terms are in A.P.

1. This statement is true. By definition, a sequence is in Harmonic Progression (H.P.) if the reciprocals of its terms form an Arithmetic Progression (A.P.).

### Conclusion
- **Statement 1** is **false** because the sum of the reciprocals of the first n odd numbers is \( \frac{n^2}{2} \), not \( n^2 \).
- **Statement 2** is **true** as it correctly defines H.P.

Thus, the final conclusion is that Statement 1 is false, and Statement 2 is true.

### Final Answer
- **Statement 1:** False
- **Statement 2:** True