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For all n ge 1 prove that 1^(2)+2^(2)+...

For all `n ge 1` prove that
`1^(2)+2^(2)+ 3^(2)+4^(2)+….+n^(2)= (n(n+1)(2n+1))/(6)`

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

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Prove that by using the principle of mathematical induction for all n in N : 1^(2)+3^(2)+5^(2)+...(2n-1)^(2)= (n(2n-1)(2n+1))/(3)

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The sum of first n terms of the series 1^(2) + 2.2^(2) +3^(2) + 2. 4^(2) + 5^(2) + 2. 6^(2) + "........." is ( n ( n + 1)^(2))/( 2) when n is even. When, n is odd, the sum is :

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OSWAAL PUBLICATION-SOLVED PAPER 2019-2-EXERCISE
  1. Verify by the method of contradiction that sqrt(2) is irrational .

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

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  3. One card is drawn from a well shufflied deck of 52 cards.If each out c...

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

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  5. A fair coin 1 marked on one face & 6 on the other face & a fair die ar...

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  6. A fair coin 1 marked on one face & 6 on the other face & a fair die ar...

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  7. Define a signum function. Write range, also draw the graph of the func...

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

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  9. For all n ge 1 prove that 1^(2)+2^(2)+ 3^(2)+4^(2)+….+n^(2)= (n(n+1)...

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  10. Solve the following system of inequations in 2 variables graphically: ...

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

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

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  13. Find the coordinates of the foot of the perpendicular from the point (...

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  14. Derive the formula to find the co-ordinates of a point which divide th...

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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. (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 derivative of (x^(5) - cos x)/(sin x) with respect to x.

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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 sum to n terms of the series 3 xx 8 + 6 xx 11 + 9 xx 14 + ....

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