The value of (1 / log₂ n) + (1 / log₃ n) + (1 / log₄ n) + ... + (1 / log₁₀ n) is:

Model Answer & Options

Source: Extra Practice

log_n (10!)

log₁₀ (n!)

1 / log_n (10!)

log_n (55)

Explanation

Using the property 1 / log_a b = log_b a, the expression transforms to: log_n 2 + log_n 3 + log_n 4 + ... + log_n 10. By the product rule log x + log y = log(xy), this becomes log_n (2 * 3 * 4 * ... * 10). Since 1 * 2 * ... * 10 is 10!, the expression equals log_n (10!). Option A is correct.

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