`log2+log(1+1/2)+log(1+1/3)+...........+log(1+1/(n-1))=`

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the value of log x+log(1+(1)/(1+x))+log(1+(1)/(2+x))+............+log(1+(1)/(n-1+x))

log_(a)(1-(1)/(2))+log_(a)(1-(1)/(3))+......log_(a)(1-(1)/(n))

Assuming the base as 10,prove that log(1+1/2)+log(1+1/3)+log(1+1/4)+….+log(1+1/19)=1

If ngt1 then prove that 1/(log_2 n )+1/(log_3 n)+.................+1/log_(53) n =1/(log_(53!) n

Find the value of the followings log_(a)(2)+log_(a)(1+(1)/(2))+log_(a)(1+(1)/(3))+...+log_(a)(1+(1)/(n))

Find the value of the followings log_(a)(2)+log_(a)(1-(1)/(2))+log_(a)(1-(1)/(3))+...+log_(a)(1-(1)/(n))

If n>1 then prove that (1)/(log_(2)n)+(1)/(log_(3)n)+............+((1)/(log_(53)n)=(1)/(log_(53!)n)

Prove log a + log a^(2) + "log" a^(3) +……..+ log a^(n) = (n (n + 1))/(2) log a