Show that `(n +1) ("^(n)P_r)` = `(n - r + 1) ["^((n +1))P_r]`

Show that : (n !) / (r ! (n - r) !) + (n !) / ((r - 1) ! (n - r + 1) !) = ((n + 1) !) / (r ! (n - r +1) !)

Find x if ^(n)P_r = x ^(n)C_r

If p, q, r, s are in G.P, show that (p^n + q^n) , (q^n + r^n) , (r^n + s^n) are also in G.P

Find n if, ^(2n)C_(r-1) = ^(2n)C_(r+1)