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Using mathematical induction prove that,...

Using mathematical induction prove that,
`"tan"^(-1)(x)/(1*2+x^(2))+"tan"^(-1) (x)/(2*3+x^(2))+...+ "tan"^(-1) (x)/(n*(n+1)+x^(2))+"tan"^(-1) x-"tan"^(-1) (1)/(n+1) "for all" n in NN`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Find the differential coefficient of: x^(5)+4x

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  2. Find the differential coefficient of: x^(2x)

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  3. Using mathematical induction prove that, "tan"^(-1)(x)/(1*2+x^(2))+"...

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  4. Using mathematical induction prove that, "tan"^(-1)(1)/(3)+"tan"^(-1...

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  5. Using mathematical induction prove that, tan^(-1)((1)/(2*1^(2)))+tan...

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  6. If (1+x+x^(2))^(n)=a(0)+a(1)+x+a(2)x^(2)+...+a(2n)x^(2n), show that a(...

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  7. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Find the value of ...

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  8. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(1)-(1)...

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  9. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that 1^(2)*C...

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  10. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(0)^(2)...

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  11. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that (2^(2)*C...

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  12. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) For all values of ...

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  13. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(1)^(2)...

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  14. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) show that (C(0))^(...

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  15. Show that the sum of the coefficient of first (r+1) terms in the expan...

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  16. Show that 4^(m)[ 1+(m)/(2)+(m(m+1))/(2*4)+(m(m+1)(m+2))/(2*4*6)+...] ...

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  17. It is given that n is an odd integer greater than 3 but n is not multi...

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  18. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n)x^(n) show that, 1^(2)*C...

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  19. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n)x^(n) show that, C(0)-2^(...

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  20. Using binomial theorem for a positive integral index, prove that (2^(3...

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