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

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

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  • MODEL PAPER (11)

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

Prove the following 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 .

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

By the Principle of Mathematical Induction, prove the following for all n in N : 1.2+2.2^2 +3.2^3+.....+ n.2^n= (n-1)2^(n+1)+2 .

By the Principle of Mathematical Induction, prove the following for all n in N : 1.3+2.3^2 +3.3^3+.....+ n.3^n= ((2n-1)3^(n+1)+3)/4 .

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 2.3^2 + 3.3^3 +... + n.3^n =((2n-1)3^(n+1) +3)/4 .

By the Principle of Mathematical Induction, prove the following for all n in N : 1^2+2^2+3^2+ .......... + n^2> n^3/3 .

By the Principle of Mathematical Induction, prove the following for all n in N : 1/1.3+1/3.5+1/5.7+......+ 1/((2n -1)(2n +1))= n/(2n +1) .

JBD PUBLICATION-MODEL PAPER (12)-EXERCISE
  1. Let A={a,b,c} and B={1,2,3}. Find the number of relations from A into ...

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  2. Show tha: cos6A=32cos^6A-48cos^4A+18cos^2A-1

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

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  4. If ^nC3=56 and ^nP3=336, find n .

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  5. The English alphabet has 5 vowels and 21 consonants. How many words wi...

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  6. The sum of two numbers is 6 times their G.M. show that numbers are in ...

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  7. Between 1 and 31, n A.M's have been inserted in sucha a way that the r...

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  8. In which ratio is the line joining the points (1,3) and (2,7) is divid...

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  9. Find the equation of hyperbola whose foic are (0, pm12) and length of ...

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  10. Evaluate:underset(xrarr0)lim (1-cos2x)/(3tan^2x)

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  11. Differentiate: (acos x+bsinx+c)/(sinx) w.r.t.x.

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  12. Three coins are tossed once. Find the probability of getting at least ...

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  13. Three coins are tossed once. Find the probability of getting at most t...

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  14. If (x + iy)^3 = u + iv, then show that u/x +v/y = 4(x^2 - y^2)

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  15. Find the square root fo 1 - i.

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  16. Find all pairs of consecutive odd positive integers both of which are ...

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  17. Solve the given inequality -5 < (x - 2)/5 le 0

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  18. Find underset(xrarr0)f(x) where f(x)={(2x+3, xle0),(3(x+1), x>0):}

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  19. Find the derivative of (sin x + cos x) from the first principle.

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  20. Find the mean deviation from mean:

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