If `a_1,a_2,a_3,.....,a_(n+1)` be `(n+1)` different prime numbers, then the number of different factors (other than1) of `a_1^m.a_2.a_3...a_(n+1)`, is

If a_(1),a_(2),a_(3),......,a_(n+1) be (n+1) different prime numbers,then the number of different factors (other than 1) of a_(1)^(m)*a_(2)*a_(3)...a_(n+1), is

If a_1, a_2, a_3,...a_n are in A.P with common difference d !=0 then the value of sind(coseca_1 coseca_2 +cosec a_2 cosec a_3+...+cosec a_(n-1) cosec a_n) will be

Statement-1 : If a_1,a_2,a_3 ,….. a_n are positive real numbers , whose product is a fixed number c, then the minimum value of a_1+a_2+…. + a_(n-1)+2a_n is n(2C)^(1/n) Statement-2 :A.M. ge G.M.

If a_1,a_2,a_3,.....,a_n are in AP where a_i ne kpi for all i , prove that cosec a_1* cosec a_2+ cosec a_2* cosec a_3+...+ cosec a_(n-1)* cosec a_n=(cota_1-cota_n)/(sin(a_2-a_1)) .

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If a_1,a_2,a_3,....a_n and b_1,b_2,b_3,....b_n are two arithematic progression with common difference of 2nd is two more than that of first and b_(100)=a_(70),a_(100)=-399,a_(40)=-159 then the value of b_1 is

If a_1,a_2,a_3,...,a_n be in AP whose common difference is d then prove that sum_(i=1)^n a_ia_(i+1)=n{a_1^2+na_1d+(n^2-1)/3 d^2} .