Find the value of the following
`(- sqrt(-1))^(4n+3), n in N`

Evaluate the following ^(n+1)C_n

Find the value of n such that 3nP_4 = 5.(n-1)P_4 , n>4

Find the value of n such that (n-1)P_3 : nP_4=1:9

Find the value of n, if 12 xx ^((n-1))P_3= 5 xx ^((n+1))P_3

Find the sum to n terms of the series in the following n^ (th) terms is given by n(n+1)(n+4)

Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n) may be the geometric mean between a and b

Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n) may be the G. M. between a and b.

Find the sum of the series 1.n + 2 .(n-1) + 3.(n-2) + cdots + ( n-1) .2 + n.1.

The set of positive values of n for which (sqrt((1+cos 30^(@))/(2))+ i sqrt((1-cos 30^(@))/(2)))^(n) is real, is