IIT JEE , AIEEE Forum - Mathematics , Algebra - TIPS' TRIPLET

Avinash_Bhat

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

Avinash_Bhat

I HOPE THESE WOULD HELP YOU, A BIT ATLEAST...........................