[(oo)tan varepsilon log_(n-1)n*log_(n)(n+1),],[log_(n+1)(n+2),-1log_(n^(k)-1)]

lim_(n->oo)[log_(n-1)(n)log_n(n+1)*log_(n+1)(n+2).....log_(n^k-1) (n^k)] is equal to :

sum_(n=1)^(n)(1)/(log_(2)(a))

if quad 0,c>0,b=sqrt(ac),a!=1,c!=1,ac!=1a>dn>0 then find an expression for (log_(a)n-log_(b)n)/(log_(b)n-log_(c)n) in terms of log_(a)n and log_(c)n

The value of N satisfying log_(a)[1+log_(b){1+log_(c)(1+log_(p)N)}]=0 is

The value of N satisfying log_(a)[1+log_(b){1+log_(c)(1+log_(p)N)}]=0 is

If N = n!(n in N, n gt 2) , then find lim_(N rarr oo)[(log_(2)N)^(-1) + (log_(3)N)^(-1)+…+(log_(n)N)^(-1)]