XAT 2014 — QA & DI Question 22

Simple EquationsEasy

The value of the expression:

$\sum_{i = 2}^{100} \frac{1}{\log_{i} 100!} is :$

Answer & solution

Correct answer: 1

A
0.01
B
0.1
1
D
10
E
100

Solution

$\sum_{i = 2}^{100} \frac{1}{\log_{i} 100!} = \sum_{i = 2}^{100} \log_{100!} 2 + \log_{100!} 3 + \log_{100!} 4 + . . . + \log_{100!} 100$

$= \log_{100!} 100! = 1$

Hence, option (c).

Related Simple Equations questions

See all Simple Equations questions →

XAT 2014 QA & DI Q22: The value of the expression: ∑ i = 2 100 1 log i 100 ! is : — Solution | TheCATExam