(2) If n > 3 then prove that C0 ab - C1(a - 1) + C2 (a - b) (b - 2) - ...............+ (-1) n Cn = 0 Ans Now, (1 + x)n = 1 + nx +

Also show that nn-1 > (n + 1)n ; 3 , Ans . We get an = = 1 + n + ..................... = 1 + 1 + + ..............

Dumb Question Why we had an interval in answer ? Ans . Well we have the situation | x | 2 and So, | x |

(9) If is an odd natural lnumber then what is the value Of ? Ans Since n is odd, the number of terms will be n + 1 which is even, Now since is an integer

Introduction (3) Find the digit at unit place in the number . 16 1986 + 111986 - 61986. ? And Let E = 16 1986 + 111986 - 61986 So, E = (10 + 6)n + (1 + 10)n - 6 n where N = 1986 =...

Illustration 8 If (3 + 4x)n = P0+ P1x + P2x2 +...+ Pnxn then prove that (Po - P2 + P4...)2 + (P1 - P3+ P5 ....)2 = 25n Ans . Let us

Illustration 5 Prove that C02 + C12 + C22+..............Cn2 = Ans : We know . (1 + x)n = C0+ C1 C2 x2.......+Cn-1xn-1 + Cnxn Also. (x + 1)n = C0 xn + C1