
Shortcut Trick
Statement A: Telescoping series Σ (1/n2 − 1/(n+1)2) = 1 − 1/100 = 0.99 (False, given 0.09).
Statement B: Simplified sum [x(x+1) + (x−1) − 2x] / (x2−1) = (x2−1) / (x2−1) = 1 (True).
Statement C: BODMAS result 3.8 − (6 × 3) + 20 = 5.8 (False, given 5.6).
Statement D: Algebraic simplification (a2−b2)/(a+b) = a−b = 3.63 − 2.37 = 1.26 (False, given 6).
Only Statement B is mathematically correct.
∴ The correct answer is B only.

Alternate Method
Given: Statements A, B, C, D.
Formula Used:
- Telescoping Series: 1/(n2 × (n+1)2) = (1/n2 − 1/(n+1)2)/(2n+1).
- a2 − b2 = (a − b)(a + b).
- BODMAS rule for order of operations.
x/(x−1) + 1/(x+1) + 2x/(1−x²) Simplified Value of B = 1
Checking Statement A:
⇒ Term Tn = (2n+1) / (n2 × (n+1)2) = 1/n2 − 1/(n+1)2
⇒ Sum = (1/12 − 1/22) + (1/22 − 1/32) + ... + (1/92 − 1/102)
⇒ Sum = 1 − 1/100 = 0.99 ≠ 0.09. (Incorrect)
Checking Statement B:
⇒ x/(x−1) + 1/(x+1) + 2x/(1−x2) = x/(x−1) + 1/(x+1) − 2x/(x2−1)
⇒ [x(x+1) + 1(x−1) − 2x] / (x2−1) = [x2 + x + x − 1 − 2x] / (x2−1)
⇒ (x2 − 1) / (x2 − 1) = 1. (Correct)
Checking Statement C:
⇒ 3.8 − (4.2 ÷ 0.7 × 3) + 5 × 2 ÷ 0.5
⇒ 3.8 − (6 × 3) + 10 ÷ 0.5 = 3.8 − 18 + 20 = 5.8 ≠ 5.6. (Incorrect)
Checking Statement D:
⇒ (3.632 − 2.372) / (3.63 + 2.37) = (3.63 − 2.37)(3.63 + 2.37) / (3.63 + 2.37)
⇒ 3.63 − 2.37 = 1.26 ≠ 6. (Incorrect)
∴ The correct answer is B only.

Additional Information
Telescoping Series
A series where most terms cancel out, leaving only the first and last parts. General form often looks like Σ[f(n) − f(n+1)].
Algebraic Identity: Difference of Squares
The expression a2 − b2 is always equal to (a − b)(a + b), which helps in simplifying complex divisions.
BODMAS Rule
Determines the sequence of operations: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction.
Rational Expressions
Adding or subtracting fractions with variables requires finding a common denominator, often by factoring the existing denominators.