If Dr=|(2/2 r-1) 3 0 (1/2 r+1)| then displaystyle∑r=1n Dr equals

Question

If Dr=|(2/2 r-1) 3 0 (1/2 r+1)| then displaystyle∑r=1n Dr equals (A) (n/2 n+1) (B) (1/2 n+1) (C) (2 n/2 n+1) (D) (2 n-1/2 n+1)

Tardigrade Admin · Accepted Answer

Dr=(2/(2 r-1)(2 r+1))=((1/2 r-1)-(1/2 r+1)) displaystyle∑ r =1 n D r =1-(1/2 n +1)=(2 n /2 n +1)

Q. If $D_{r} = ∣ ∣ \frac{2}{2 r - 1} 0 3 \frac{1}{2 r + 1} ∣ ∣$ then $r = 1 \sum n D_{r}$ equals