If the coefficients of x−7 and x−8  in the expansion of (2+13x)n  are equal then n=

In the expansion (2+13x)n (∴  Tr+1= nCr xn−r (a)r  be the general term of expansion  (x+a)n) Then Tr+1= nCr2n−r(13x)r= nCr2n−r3rx−r So, coefficient of x−r= nCr2n−r3r  ⇒    Coefficient of x−7= nC72n−737 And   coefficient of x−8  = nC82n−838  According to problem coefficients are equal hence nC7 2n−737=nC8 2n−838⇒nC8nC7=38 2n−737 2n−8⇒nC8nC7=6 ⇒    nC8nC7=6  ⇒  n−78=6  (∴  nCrnCr−1=n−r+1r) ∴   n=55