Please solve this 

Asked by aastharoy997 | 4th Apr, 2020, 03:29: PM

Expert Answer:

If n=37!, then find the value of 1/log2n + 1/log3n +... +1/log37n
Solution:
fraction numerator 1 over denominator log subscript 2 space n end fraction plus fraction numerator 1 over denominator log subscript 3 space n end fraction plus... plus fraction numerator 1 over denominator log subscript 37 space n end fraction
equals fraction numerator 1 over denominator begin display style fraction numerator log space n over denominator log space 2 end fraction end style end fraction plus fraction numerator 1 over denominator begin display style fraction numerator log space n over denominator log space 3 end fraction end style end fraction plus... plus fraction numerator 1 over denominator begin display style fraction numerator log space n over denominator log space 37 end fraction end style end fraction
equals fraction numerator log space 2 over denominator log space n end fraction plus fraction numerator log space 3 over denominator log space n end fraction plus... plus fraction numerator log space 37 over denominator log space n end fraction
equals fraction numerator log space 2 plus log space 3 plus... plus log space 37 over denominator log space n end fraction
equals fraction numerator log open parentheses 2 cross times 3 cross times... cross times 37 close parentheses over denominator log space n end fraction space.... space open parentheses S i n c e comma space log space a plus log space b equals log space a b close parentheses
equals fraction numerator log space 37 factorial over denominator log space 37 factorial end fraction space equals space 1
H e n c e comma space fraction numerator 1 over denominator log subscript 2 space n end fraction plus fraction numerator 1 over denominator log subscript 3 space n end fraction plus... plus fraction numerator 1 over denominator log subscript 37 space n end fraction equals 1

Answered by Renu Varma | 5th Apr, 2020, 02:06: PM