Can you answer these questions

1)  IF 3 CONSEQUTIVE BINOMIAL COEFFICIENTS : ⁿC_r-1 , ⁿC_r , ⁿC_r+1 : ARE IN A.P., THEN

  

                                                   r  =  1/2 (n    (n + 2) )

 

    BE AWARE THAT : 3 CONSEQUTIVE BINOMIAL COEFFICIENTS ARE NEVER IN G.P. OR H.P. AND THAT 4 CONSEQUTIVE BINOMIAL COEFFICIENTS ARE NEVER IN A.P.

 

 

2)  THE TERM IN x^m IN THE EXPANSION OF ( ax^p + b/x^q)ⁿ IS T_r+1 WHERE :

 

                                                   r  = (np - m) / (p + q)

 

     OBVIOUSLY, THE TERM INDEPENDENT OF 'x' IS T_r+1 WHERE :

 

                                                   r  =  np / (p +q)

 

 

3)  THE NO. OF DISTINCT TERMS IN THE EXPANSION OF :

      (a₁ + a₂ + a₃ + ................ + a_m)ⁿ IS :

 

                                          ^n+m-1 C _m-1  

ANSWER WILL BE GIVEN TO THESE QUESTIONS WITHIN FEW DAYS. FOR ANSWERS PLEASE FOLLOW THE LITTLE GANESHA FREQUENTLY