Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Let be a positive integer and _r = vmatrix 2r-1 & ^m C_r & 1 m^2-1 & 2^m & m+1…
MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants
Problem Let m m m Δ r = ∣ 2 r − 1 m C r 1 m 2 − 1 2 m m + 1 sin 2 ( m 2 ) sin 2 ( m ) sin 2 ( m + 1 ) ∣ ( 0 ≤ r ≤ m ) . \Delta_r = \begin{vmatrix} 2r-1 & {}^m C_r & 1 \\ m^2-1 & 2^m & m+1 \\ \sin^2(m^2) & \sin^2(m) & \sin^2(m+1) \end{vmatrix} \quad (0 \leq r \leq m). Δ r = 2 r − 1 m 2 − 1 sin 2 ( m 2 ) m C r 2 m sin 2 ( m ) 1 m + 1 sin 2 ( m + 1 ) ( 0 ≤ r ≤ m ) . ∑ r = 0 m Δ r \sum_{r=0}^m \Delta_r ∑ r = 0 m Δ r m 2 − 1 m^2-1 m 2 − 1 2 m 2^m 2 m 2 m sin 2 ( 2 m ) 2^m \sin^2(2^m) 2 m sin 2 ( 2 m ) Browse the problem library