The correct answer is D: 2/15. Each term = 1/((2n−1)(2n+1)) = (1/2)(1/(2n−1) − 1/(2n+1)); telescoping from n=2 to n=7 gives (1/2)(1/3 − 1/15) = (1/2)(12/45) = 2/15.
A.3/15
B.6/15
C.4/15
D.2/15✓ Correct
Explanation
Each term = 1/((2n−1)(2n+1)) = (1/2)(1/(2n−1) − 1/(2n+1)); telescoping from n=2 to n=7 gives (1/2)(1/3 − 1/15) = (1/2)(12/45) = 2/15.
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