Show that `4^(m)[ 1+(m)/(2)+(m(m+1))/(2*4)+(m(m+1)(m+2))/(2*4*6)+...]`
`7^(m)[ 1+(m)/(7)+(m(m-1))/(7*14)+(m(m-1)(m+2))/(7*14*21)+...]`

Show that m_4 ge m_2^2 .

m(m-1)(m-2)...3.2.1=

Sin A=m sin B,show that , tan((A-B)/2)=(m-1)/(m+1)tan((A+B)/2)

Factorise : m^(2)+(1)/(m^(2))+2-2m-(2)/(m)

sum_(m=1)^(n) tan^(-1) ((2m)/(m^(4) + m^(2) + 2)) is equal to

Simply {(a^m)^(m-1/m)}^(1/(m+1))

Simplify : ((4^(m+(1)/(4))xxsqrt(2.2^m))/(2.sqrt(2^(-m))))^((1)/(m)) .

The lines y=m_1x ,y=m_2xa n dy=m_3x make equal intercepts on the line x+y=1. Then (a) 2(1+m_1)(1+m_3)=(1+m_2)(2+m_1+m_3) (b) (1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3) (c) (1+m_1)(1+m_2)=(1+m_3)(2+m_1+m_3) (d) 2(1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3)

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}

Show that the straight line x cosalpha+y sin alpha=p is a tangent to the curve (x^(m))/(a^(m))+(y^(m))/(b^(m))=1 , if (a cos alpha)^((m)/(m-1))+(b sin alpha)^((m)/(m-1))=p^((m)/(m-1))