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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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    OSWAAL PUBLICATION|Exercise EXERCISE|55 Videos

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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.

1^(2)+2^(2)+3^(2)+............+n^(2)=(n(n+1)(2n+1))/6 forall n in N.

OSWAAL PUBLICATION-SAMPLE PAPER 2-EXERCISE
  1. A and B are events such that P(A) =0.42,P(B) =0.48 and P(A and B) =0.1...

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  2. A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and ...

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  3. A and B are events such that P(A) =0.42,P(B) =0.48 and P(A and B) =0.1...

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

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

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  6. Define an identity function . Draw the graph of identify function and ...

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  7. (cos 4x+cos3x+cos2x)/(sin 4x+sin3x+sin2x)=cot3x

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  8. 1/1.2+1/2.3+1/3.4+…………….+1/(n(n+1))=n/(n+1) forall n in N.

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  9. Solve the inequalities :2x+3yle12,xge2,yge2 graphically.

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  10. A committee of 7 has to be formed from 9 boys and 4 girls. In how many...

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  11. A committee of 7 has to be formed from 9 boys and 4 girls. In how many...

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  12. A committee of 7 has to be formed from 9 boys and 4 girls. In how many...

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  13. Show that the middle term in the expansion of (1+x)^(2n) is 1.3.5…(2n...

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  14. Derive the equation of a straight line passing through the point(x0,y0...

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  15. Prove that underset(xrarr0)lim(sinx/x=1) ?

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

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

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

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  19. Define hyperbola as a set of points derive its equation in the form (...

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  20. Find the derivative of (x + cos x)/(tan x) with respect to x

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