QA – Placement Quizzes | Progressions | Question 15

The value of the expression ¹⁰⁰∑_i=2 1/log_i100! is:
(A) 0.01
(B) 0.1
(C) 1
(D) 10

Answer: (C)
Explanation: The expression ¹⁰⁰∑_i=2 1/log_i100! can be rewritten as:
1/log₂100! + 1/log₃100! + … + 1/log₁₀₀100!
= log_100!2 + log_100!3 + … + log_100!100
= log_100!2*3*…*100
= log_100!100!
= 1.
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