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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
