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If-m-is-a-positive-integer-and-r-determinant-2r-1-m-C-r-1-m-2-1-2-m-m-1-sin-2-m-2-sin-2-m-sin-2-m-1-then-the-value-of-r-0-m-r-i




Question Number 15191 by arnabpapu550@gmail.com last updated on 08/Jun/17
If m is a positive integer and  △_r = determinant (((   2r−1),(^m C_r ),(        1)),((  m^2 −1),(    2^m ),(   m+1)),((sin^2 (m^2 )),(sin^2 (m)),(sin^2 (m+1))))  then the value of   Σ_(r=0) ^m △_r    is
$$\mathrm{If}\:{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{and} \\ $$$$\bigtriangleup_{{r}} =\begin{vmatrix}{\:\:\:\mathrm{2}{r}−\mathrm{1}}&{\:^{{m}} {C}_{{r}} }&{\:\:\:\:\:\:\:\:\mathrm{1}}\\{\:\:{m}^{\mathrm{2}} −\mathrm{1}}&{\:\:\:\:\mathrm{2}^{{m}} }&{\:\:\:{m}+\mathrm{1}}\\{\mathrm{sin}^{\mathrm{2}} \left({m}^{\mathrm{2}} \right)}&{\mathrm{sin}^{\mathrm{2}} \left({m}\right)}&{\mathrm{sin}^{\mathrm{2}} \left({m}+\mathrm{1}\right)}\end{vmatrix} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\underset{{r}=\mathrm{0}} {\overset{{m}} {\sum}}\bigtriangleup_{{r}} \:\:\:\mathrm{is} \\ $$
Commented by arnabpapu550@gmail.com last updated on 08/Jun/17
please give me answer soon
$$\mathrm{please}\:\mathrm{give}\:\mathrm{me}\:\mathrm{answer}\:\mathrm{soon} \\ $$

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