sum_(r=0)^(n-1)log_(2)((r+2)/(r+1))=prod_(r=10)^(99)log_(r)(r+1)

If quad sum_(r=7)^(2400)log_(7)((r+1)/(r)),M=prod_(r=2)^(103)log_(r)(r+1) and N=sum_(r=2)^(2011)((1)/(log_(r)P)) where P=(1.2.34.......2011), then

sum_(r= 2)^(43) (1)/(log_(r)n) =

(1+x)^(n)=sum_(r=0)^(n)a_(r)x^(r)&b_(r)=1+(a_(r))/(a_(r-1))&prod_(r=1)^(n)b_(r)=((101)^(100))/(100!) then equals to: 99(b)100(c)101(d) None of these

sum_(r=0)^(n)(-1)^(r)*^(n)C_(r)(1+r log_(e)10)/((1+log_(e)10^(n))^(r))=

If a_(n)=sum_(r=1)^(n)log_(e)(a^(r));a>0&S_(n)=sum_(r=1)^(n)a_(r) then minimum value of n such that sum is greater than 1335log_(e)a^(n) is

sum_(r=1)^(89)log_(3)(tan r^(@)))