" If "(np_(x-1))/(a)=(n_(px))/(b)=(n_(p_(i+1)))/(c)

If n_(P_(r-1))/(a)=(n_(P_(r)))/(b)=(n_(P_(r+1)))/(c) ," then which of the following holds good

If (.^(n)P_(r-1))/(a)=(.^(n)P_(r))/(b)=(.^(n)P_(r+1))/(c) prove that , b^(2)=a(b+c)

If n_(p_(r-1))/a=n_(p_r)/b=n_(p_(r+1))/c ,then show that b^2=a(b+c)

If the number of permutations of n different things taken r at a time be denoted by nP_(r) show that (nP_(1))/(1!)+(nP_(2))/(2!)+(nP_(3))/(3!)+......+(nP_(n))/(n!)=2^(n)-1

If (nP_(r-1))/a=(nP_r)/b=(nP_(r+1))/c then show that b^2-ab-ac=0

Find the value of n such that (i)^nP_(5)=42^(n)P_(3),n>4(nP_(4))/(n-1P_(4))=(5)/(3),n>4

If ""^(nP_(r)=""^(n)P_(r+1) and ""^(n)C_(r)=""^(n)C_(r-1) find n and r.