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Question: Find the sum of the following series:

3/4 + 5/36+ 7/144+9/400 + ……..+ ∞

Answer Options:

a. 1/2
b. 2/3
c. 1
d. 2

Answers and Explanations

Answer: 3

Solution:

The series can be re-written as:

= 3/(1×2)2 + 5/(2×3)2 + 7/(3×4)2 +9/(4×5)2 + ……..+ ∞

= 22 – 12/ (1×2)2 + 32 – 22/(2×3)2 + 52 – 42/(4×5)2 +………………….∞

= (1/12 – 1/22) + (1/22 – 1/32) +(1/32 – 1/42)+  …….∞

= 1

OB-CAT-MOCK-AD-POST




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