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Prove by mathematical induction 1+2+3+……...

Prove by mathematical induction `1+2+3+……+n(n(n+1))/(2)`.

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Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

Prove the following by the principle of mathematical induction: \ 1. 3+2. 4+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove by the mathematical induction x^(2n)-y^(2n) is divisible by x+y

Prove that by using the principle of mathematical induction for all n in N : (1)/(2.5)+ (1)/(5.8) + (1)/(8.11)+ ...+(1)/((3n-1)(3n+2))= (n)/(6n+4)

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OSWAAL PUBLICATION-SAMPLE PAPER 1-EXERCISE
  1. Two students Anil and Ashima appeared in an examination . The probabi...

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  2. A letter is chosen at random from the word "ASSASSINATION" . Find the ...

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  3. A letter is chosen at random from the word 'ASSASSINATION' Find the pr...

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  4. In a survey of 600 students in a school, 150 students were found to be...

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  5. If the function from f:R rarr R is defined as f(x)=x^2,then draw the g...

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  6. Prove that : (sin 5x-2sin3x+sinx)/(cos5x-cosx)=tanx

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  7. Prove by mathematical induction 1+2+3+……+n(n(n+1))/(2).

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  8. Solve graphically 2x+y ge 4, x+y le 3, 2x-3y le 6 x ge 0, y ge 0

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  9. A group consists of 4 girls and 7 boys .In how many ways can a team o...

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  10. A group consists of 4 girls and 7 boys. In how ways can a team of 5 m...

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  11. A group consists of 4 girls and 7 boys. In how many ways can a team of...

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  12. State and prove Binomial theorem for a positive integer index.

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  13. Derive a formula for the angle between two lines with slopes m(1) and ...

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  14. Derive the formula for the distance between two points(x1,y1,z1) and (...

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  15. Prove thatunderset(thetararr0)lim(Sintheta)/theta =1 , (theta being in...

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  16. Find the mean deviation about the mean for the following data.

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  17. Prove Geometrically cos(x+y)=cosx,cosy-sinx.siny and hence prove that ...

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  18. (b)Find the sum of first n terns of the series 1^2+2^2+……+n^2.

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  19. Derive the equation of the ellipse in the form (x^(2))/(a^(2))+(y^(2))...

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  20. Find the derivative of(x^(2)-cosx)/sinx with respect to x ?

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