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If m is a positive integer and Dr=|[2r-...

If `m` is a positive integer and `D_r=|[2r-1,m_(C_r),1],[m^2-1, 2^m, x+1],[sin^2(m^2),sin^2(m),sin^2(m+1)]| `Prove that`` `sum_(r=0)^m D_r=0`

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If m is a positive integer and D_r=|(2r-1,\ ^m C_r,1),(m^2-1, 2^m ,m+1),(sin^2(m^2),sin^2(m),sin^2(m+1))| . Prove that sum_(r=0)^m D_r=0 .

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Let t be a positive integer and |((2t-1),m^2-1,cos^2(m)),(mC_t,2^m,cos^2(m)),(1,m+1,cos(m^2))| then the value of sum_(t=0)^m Delta_t is equal to

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If r<1 and positive and m is a positive integer,shew that (2n+1)r^(m)(1-r)<1-r^(2m+1) Hence shew that nr^(n) is indefinitely small when en isindefinitely great.

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