Which of the following statement(s) is/are True?
I. 1/1×3 + 1/3×5 + 1/5×7 + .....+ 1/11×13 = 12/13
II. 1/1×2 + 1/2×3 + 1/3×4 + ......+ 1/12×13 = 12/13
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2, i.e. Only II
I. 1/1×3 + 1/3×5 + 1/5×7 + .....+ 1/11×13 = 12/13
LHS= 1/2[ 1 - 1/3 + 1/3 -1/5 + 1/5 -1/7 + 1/7 ....1/11 - 1/13]
=1/2(1 - 1/13)
= 6/13 not equal to 12/13 (false)
II. 1/1×2 + 1/2×3 + 1/3×4 + ......+ 1/12×13 = 12/13
LHS = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 ..... + 1/12 - 1/13
= 1 - 1/13
= 12/13 (true)