Identify the correct mathematical statement(s):

1.The expression 3/4 + 5/36 + 7/144 + ... + 17/5184 + 19/8100 is equal to 0.09.

2.The value of x/(x-1) + 1/(x+1) + 2x/(1-x^2) is 1.

3.The value of 3.8 - (4.2 / 0.7 x 3) + 5 x 2 / 0.5 is 5.6.

4.The value of ((3.63)^2 - (2.37)^2)/(3.63 + 2.37) is equal to 6.

A1 & 3 only

B2 only ✓ Correct

C2 & 4 only

D3 & 4 only

Correct answer: (B) 2 only

Explanation

Only Statement 2 is correct.

Statement 2 : x/(x-1) + 1/(x+1) + 2x/(1-x^2) combines over (x-1)(x+1).

The numerator becomes x^2 - 1, so the value is (x^2-1)/(x^2-1) = 1, which holds.

Statement 1 fails : that series telescopes to 1 - 1/100 = 0.99, not 0.09.

Statement 3 fails : 3.8 - (6 x 3) + 10/0.5 = 3.8 - 18 + 20 = 5.8, not 5.6.

Statement 4 fails : (3.63^2 - 2.37^2)/(3.63 + 2.37) = 3.63 - 2.37 = 1.26, not 6.

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