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If u(r)=(1)/(r!) then show that u(0)u(...

If `u_(r)=(1)/(r!)` then show that
`u_(0)u_(n)+8u_(1)+u_(n-1)+8^(2)u_(2)u_(n-2)+...+ 8^(n)u_(n)u_(0)=(3^(2n))/(n!)`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. If n is a positive integer then using the indentiy (1+x)^(n)=(1+x)^(3)...

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  2. If S(1), S(2), S(3),...S(n) are the sums of infinite geometric series,...

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  3. If u(r)=(1)/(r!) then show that u(0)u(n)+8u(1)+u(n-1)+8^(2)u(2)u(n-2...

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  4. a series is given by the following form : 1+(x+x^(2))+(x^(3)+x^(4)+x...

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  5. If x= cos theta+i sin theta and 1+ sqrt(1-a^(2))=na, show that, (a)/(...

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  6. Show that (a+ omega +omega ^(2))(a+omega ^(2)+omega ^(4))(a+omega ^(4)...

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  7. Let z and omega tow complex number. If |z|= |omega| and areg (z) +arg...

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  8. If z(1)+z(2) are two complex number and |(barz(1)-2bar z(2))/(2-z(1)ba...

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  9. If x+iy moves on the line 3x+4y+5=0, prove that the minimum value of ...

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  10. If |z^(2)|=9|z|, find the maximum and minimum values of |z|.

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  11. Find the greatest value of |z| when |z-(6)/(z)|=2,z being a complex nu...

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  12. Find the least value of |z+(1)/(z)| if |z| ge 3 (z being a complex ...

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  13. If the roots of the equation ix^(2)-(b^(2)+c^(2))x+(c^(2)+d^(2))^(2)=0...

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  14. If one root of the equation ax^(2)-2ibx-ic=0 be square of the other, t...

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  15. Solve (7y^(2)+1)/(y^(2)-1)-4 ((y^(2)-1)/(7y^(2)+1))=-3

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  16. Solve (x-(x)/(x+1))^(2)+2x((x)/(x+1))=3

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  17. If alpha and beta are the roots of ax^(2)+bx+cid=0 find the equation ...

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  18. Show that, 3^(n)-(n)/(1!)3^(n-1)+(n(n-1))/(2!)3^(n-2)-...+(-1)^(n)="...

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  19. Find the coefficient of x^(-5) in ""^(n)C(0)-""^(n)C(1) ((2x-1)/(x)...

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  20. Find the degree of theexpansion, {x+(x^(3)-1)^(1//2)}^(5)+{x-(x^(3)-...

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