Evaluate :


To find: Value of


Formula used: (i)


(ii) (a+b)n = nC0an + nC1an-1b + nC2an-2b2 + …… +nCn-1abn-1 + nCnbn


(a+1)6 =


6C0a6 + 6C1a5 + 6C2a4 + 6C3a3 + 6C4a2 + 6C5a + 6C6 … (i)


(a-1)6 =


6C0a6 - 6C1a5 + 6C2a4 - 6C3a3 + 6C4a2 - 6C5a + 6C6 … (ii)


Adding eqn. (i) and (ii)


(a+1)6 + (a-1)6 = [6C0a6 + 6C1a5 + 6C2a4 + 6C3a3 + 6C4a2 + 6C5a + 6C6] + [6C0a6 - 6C1a5 + 6C2a4 - 6C3a3 + 6C4a2 - 6C5a + 6C6]


2[6C0a6 + 6C2a4 + 6C4a2 + 6C6]


2


2[(1)a6 + (15)a4 + (15)a2 + (1)]


2[a6 + 15a4 + 15a2 + 1] = (a+1)6 + (a-1)6


Putting the value of a = in the above equation


= 2[6 + 154 + 152 + 1]


2[8 + 15(4) + 15(2) + 1]


2[8 + 60 + 30 + 1]


2[99]


198


Ans) 198


1