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1/1.2+1/2.3+1/3.4+…………….+1/(n(n+1))=n/(n...

`1/1.2+1/2.3+1/3.4+…………….+1/(n(n+1))=n/(n+1) forall n in N.`

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1.2+2.3+3.4+…………..+n(n+1)=n/3(n+1)(n+2) forall n in N.

1/1.4+1/4.7+1/7.10+...+1/((3n-2)(3n+1))=n/((3n+1)) forall n in N.

1/(2*5)+1/(5*8)+1/(8*11)+............1/((3n-1)(3n+2))=n/((6n+4)) forall n in N.

1+2+3+............+n=(n(n+1))/2 forall n in N.

lim_(n rarr oo) ((1)/(1.2) + (1)/(2.3) + (1)/(3.4) +…..+ (1)/(n(n+1))) is :

(1+3/1)(1+5/4)(1+7/9)...(1+((2n+1))/n^(2))=(n+1)^(2) forall n in N.

For all n ge 1 prove that (1)/(1.2)+ (1)/(2.3)+(1)/(3.4)+.....+(1)/(n(n+1))=(n)/(n+1)

1^(3)+2^(3)+3^(3)+………….+n^(3)=(n^(2)(n+1)^(2))/4 forall n in N.

1*2*3+2*3*4+...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 forall n in N.

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OSWAAL PUBLICATION-SOLVED PAPER 2016-1-EXERCISE
  1. A committee of two persons is selected from two men and two women. Wha...

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  2. A committee of two persons is selected from two men and two women. Wha...

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  3. A committee of two persons is selected from two men and two women.What...

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  4. A fair die is thrown. Describe the following events. A: a number les...

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  5. A fair die is thrown. Describe the following events. B: a number gre...

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  6. A fair die is thrown. Describe the following events. C: a multiple o...

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  7. Define modulus function, draw the graph of it, write its domain and ra...

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

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  9. 1/1.2+1/2.3+1/3.4+…………….+1/(n(n+1))=n/(n+1) forall n in N.

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  10. Solve graphically the system of linear inequalities 4x+3y le 60, y ge2...

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

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

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

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

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  15. Derive the expression for the length of the perpendicular drawn from t...

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  16. Find the coordinates of the mid-point of the line joining the points (...

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  17. Prove that underset(xrarr0)limsinx/x=1 ?

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  18. Find the sum to n terms of the series , 5+11+19+29+41…

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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. If y=(sin x+cos x)/(sin x- cos x)" find " (dy)/(dx).

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