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1^(2)+2^(2)+3^(2)+............+n^(2)=(n(...

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

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

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

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1^(2) + 1+ 2^(2) + 2 + 3^(2) + 3+"............"+n^(2) + n is equal to :

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

a+ar+ar^(2)+...+ar^(n-1)=(a(1-r^(n)))/(1-r) 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.

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OSWAAL PUBLICATION-SOLVED PAPER 2019-1-EXERCISE
  1. Find the centre and the radius of the circle x^2+y^2+8x+10y-8=0

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  2. Find the derivative of cos x from first principle.

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  3. Verify by the method of contradiction that sqrt7 is irrational number

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  4. If E and F are two events such that P(E)=1/4, P(E)=1/2 and P(E and F)=...

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  5. One card is drawn from a well shuffled deck of 52 cards.If each outcom...

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  6. One card is drawn from a well shuffled deck of 52 cards.If each outcom...

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  7. One card is drawn from a well shuffled deck of 52 cards.If each outcom...

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

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  9. Prove that cos^(2)+x+cos^(2) (x+pi/3)+cos^(2)(x-pi/3)=3/2 and hence fi...

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  10. 1^(2)+2^(2)+3^(2)+............+n^(2)=(n(n+1)(2n+1))/6 forall n in N.

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  11. Solve the following system of inequalities graphically : 5x + 4y ...

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

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  13. State and prove Bionomial theorem for any positive integer n.

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  14. Find the equation of the line, which makes intercepts -3 " and " 2 on...

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

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  16. Prove that underset (x rarr 0) lim (sin x)/x=1,where x is in radian an...

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  17. (a)Derive geometrically that cos(x+y)=cos x cos y-sin x sin y.Hence de...

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  18. (b) Find the sum to n terms of the series 1 xx 2 xx 3 + 2 xx 3 xx 4 + ...

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  19. (a)Define a parabola and derive its equation in the standard form y^2=...

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

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