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Observing that 1^(3)=1, 2^(3)=3+5, 3^(3)...

Observing that `1^(3)=1, 2^(3)=3+5, 3^(3)=7+9+11, 4^(3)=13+15+17+19`, find a general formula for the cube of natural number n.

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The correct Answer is:
`n^(3)=(n^(-2)n+1)+(n^(2)n+3)+(n^(2)-n+5)+...+(n^(2)+n-1)`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Find the square root of (a^(2))/(b^(2))+(b^(2))/(a^(2))+(1)/(2i)((a)/(...

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  2. z(1) and z(2) are two non-zero complex numbers such that z(1)^(2)+z(1)...

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  3. Observing that 1^(3)=1, 2^(3)=3+5, 3^(3)=7+9+11, 4^(3)=13+15+17+19, fi...

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  4. Obtain the sum of (1)/(x+1)+(2)/(x^(2)+1)+(4)/(x^(4)+1)+...+ (2^(n))/(...

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  5. Let A and B be two comoplex numbers such that (A)/(B)+(B)/(A)=1. Prove...

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  6. Show that the complex numbers z(1),z(2),z(3) satisfying (z(1)-z(3))/(z...

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  7. If z(1),z(2),z(3) are complex numbers such that |z(1)|=|z(2)|=|Z(3)|=|...

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  8. Show that (666 ...n "times")^(2)+(888.... N times) =(444.... 2n times)...

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  9. Let z(1)=10+6i and z(2)=4+6i. If z is complex number such that the arg...

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  10. z(1) and z(2) are two non-zero complex numbers, they form an equilater...

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  11. If the complex numbers z(1),z(2),z(3) represents the vertices of an e...

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  12. If omega is an imaginary cube root of unity. Find the value of the exp...

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  13. Find the sum of all multiples 3 or 4 between 1 and 325.

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  14. The vertices A,B,C of an isosceles right angled triangle with right an...

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  15. If n ge0 is integer, using induction method prove that, (1)/(1+x)+(2...

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  16. Find the differential coefficient of: x^(5x)

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  17. If x+y=a+b and x^(2)+y^(2)=a^(2)+b^(2), then by mathematical induction...

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  18. By the principle of mathematical induction prove that, (2^(2^(n))+1) h...

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  19. Find the differential coefficient of: x^(9)-5x^(2)+3x

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  20. Find the solution set of inequation (x-2)/(x+5) gt2.

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