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SEAMO 2027 - Paper F - SET 04 - Self-study Question 17

SEAMO · SEAMO 2027 - Paper F - SET 04 - Self-study

Question 17

Evaluate
$$\frac1{\log_2N}+\frac1{\log_3N}+\frac1{\log_4N}+\cdots+\frac1{\log_{100}N}.$$

Use real logarithms with N positive and different from 1. Compare the options as identities valid throughout that domain.
  1. $\log_N100!-2$
  2. $\log_N100!-1$
  3. $\log_{100!}N$
  4. $\log_N(100!)$
  5. $\frac1{\log_{100!}N}-1$