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Using mathematical induction prove that,...

Using mathematical induction prove that,
`"tan"^(-1)(1)/(3)+"tan"^(-1)(1)/(7)+...+ "tan"^(-1) (1)/(n^(2)+n+1) = tan^(-1) (n+1)-(pi)/(4) "for all " n in NN`.

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Explore conceptually related problems

prove that tan ^(-1)"" (1)/(4) + tan ^(-1) ""(2)/(9) + tan ^(-1) "" (1)/(5) + tan ^(-1) ""(1)/(8) =(pi)/(4).

prove that , 4 tan ^(-1) ""(1)/(5) -tan ^(-1 )""(1)/(70) + tan ^(-1) ""(1)/(99) = (pi)/(4) .

Prove that, tan^(-1) (4/3) + tan^(-1) (12/5) = pi - tan^(-1)(56/33) .

tan ^(-1) ""(1)/(3) + tan^(-1)""(1)/(7)+tan ^(-1)""(1)/(5)+tan ^(-1)""(1)/(8)=(pi)/(4)

Prove that, "tan"^(-1)(1)/(2xx1^(2))+"tan"^(-1)(1)/(2xx2^(2))+"tan"^(-1)(1)/(2xx3^(2))+…oo=(pi)/(4)

2 tan ^(-1) ""(1)/(5)+tan^(-1)"" (1)/(8)= tan ^(-1) ""(4)/(7)

Prove that tan ^(-1)"" (4)/(3)+ tan ^(-1) "" (12)/(5) =pi - tan ^(-1) "" (56)/(33) .

Show that , 4 (2 tan ^(-1) ""(1)/(3)+tan ^(-1)""(1)/(7)) =pi

Prove that, "tan"^(-1)(a)/(b)-"tan"^(-1)((a-b)/(a+b))=(pi)/(4) .

Prove the following : 2"tan"^(-1)1/2+"tan"^(-1)1/7="tan"^(-1)31/17

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Find the differential coefficient of: x^(2x)

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

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

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

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  5. 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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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. Show that the sum of the coefficient of first (r+1) terms in the expan...

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

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

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  17. 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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  18. 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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  19. Using binomial theorem for a positive integral index, prove that (2^(3...

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  20. Find the largest coefficient in the expansion of (1+x)^(n), given that...

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