If `n=1999!` then `sum_(x=1)^(1999) log_n x=`

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

If sum_(i=1)^(n)sin x_(i)=n then sum_(i=1)^(n)cot x_(i)=

If sum_(i=1)^(n)sin x_(i)=n then sum_(i=1)^(n)cot x_(i)=

Let x_(n)=3^(a+(n-1)b)(n in N and a,b are non negative integers) be an increasing geometric sequence satisfying sum_(x=1)^(8)log_(3)(x_(n))=308 and 56<=log_(3)(sum_(x=1)^(8)x_(n))<=57 ,then log_(3)(x_(5)) is greater than or equal to -

If 1+x^(2)=sqrt(3)x, then sum_(n=1)^(24)(x^(n)-(1)/(x^(n))) is equal to

If n in N, sum_(k=1)^(n)cos^(-1)(x_(k))=npi then the value of sum_(k=1)^(n)sin^(-1)(x_(k))=

Show that sum_(r=2)^(43) frac{1}{log_(r)n} = log_n (43) !

If n in N, sum_(k=1)^(n)sin^(-1(x_(k))=(npi)/2 then the value of sum_(k=1)^(n)x_(k)=