Question

If n is odd then value of $s=\frac{c_1}{c_0}-2\frac{c_2}{c_1}+3\frac{c_3}{c_2}$ ... upto n terms is

Answer 1

$\frac{{}^n{C}_r}{{}^n{C}_{r-1}}=\frac{n-r+1}{r}$

$\therefore S=\frac{C_1}{C_0}-2\frac{C_2}{C_1}+3\frac{C_3}{C_2}+......n$ terms

$=\frac{n-1+1}{1}-2\frac{n-2+1}{2}+3\frac{n-3+1}{3}+....n$ terms

$=n-(n-1)+(n-2)+.......n$ terms

Let $n=1,S=1=n$

$n=3,S=n-1$

$n=5,S=n-2$

$n=n,S=n-\frac{n-1}{2}$

$=\frac{2n-n+1}{2}=\frac{n+1}{2}$