(22." Show that: ")/((b+(1)/(a))^(m)times(b-(1)/(a))^(n))=((a)/(b))^(m+n)

Show that: (a+(1)/(b))^(m)x(a-(1)/(b))^(n)(b+(1)/(a))^(m)x(b-(1)/(a))^(n)=((a)/(b))^(m+n)

Show that: ((a+1/b)^m xx\ (a-1/b)^n)/((b+1/a)^m\ xx\ (b-1/a)^n)=(a/b)^(m+n)

Show that : ((a^(m))/(a^(-n)))^(m-n)xx((a^(n))/(a^(-1)))^(n-1)xx((a^(l))/(a^(-m)))^(l-m)=1

Show that log_(b)(1/(b^n)) = -n

Find n so that: (i) (a^(n+1)+b^(n+1))/(a^(n)+b^(n)) (ii) (a^(n)+b^(n))/(a^(n-1)+b^(n-10) may be A.M. between a and b.

Show that sum of n G.M.s between a and b is ((ab^((1)/(n+1))-ba^((1)/(n+1)))/(a^((1)/(a+1))-b^((1)/(n+1))))

If y=(x-a)^(m)(x-b)^(n) , prove that (dy)/(dx)=(x-a)^(m-1)(x-b)^(n-1)[(m+n)x-(an+bm) ].