If C_j stands for ^nC_j, then C_1C_0+ 2 C_2C_1+ 3 C_3C_2+ …+ n C_nC_n-1=

Question

Accepted Answer

Correct answer: D. (d) General term for given polinomial r ^nC_r ^nC_r-1= r n !r ! (n-r ) ! n ! (r-1 ) ! (n-r+1 ) != (n-r+1 ) Hence C_1C_0+ 2C_2C_1+ …+ nC_nC_n-1=n+ (n-1 )+ (n-2 )+ …+ [ (n )- (n-1 ) ] =n+ (n-1 )+ (n-2 )+ …+3+2+1= _k=1^nk

$If C_{j} stands for^{n} C_{j}, then \frac{C _{1}}{C _{0}} + \frac{2 \times C _{2}}{C _{1}} + \frac{3 \times C _{3}}{C _{2}} + \dots + \frac{n \times C _{n}}{C _{n - 1}} =$

Solution

More Permutations & Combinations PYQs