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If n is a positive integer, show that, ...

If n is a positive integer, show that,
`(n+1)^(2) + (n+2)^(2) + …+ 4n^(2) = (n)/(6)(2n+1)(7n+1)`

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Long Answer Type Questions)
  1. Find the sum of the following series : 1+5+12+22+35+…. to n terms.

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  2. The sum of first n terms of a series is n^(2) + an + b. Show that b = ...

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  3. If n is a positive integer, show that, (n+1)^(2) + (n+2)^(2) + …+ 4n...

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  4. Find the sum to n terms of each of the following series : (1) + (1+2...

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  5. Find the sum to n terms of each of the following series : (1^(2)) + ...

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  6. Find the sum to n terms of each of the following series : (3^(3) - 2...

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  7. Find the sum to n terms of each of the following series : (1) + (2+3...

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  8. Find the sum to n terms of each of the following series : (1)/(1.4) ...

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  9. Find the sum to n terms of each of the following series : (1)/(2.5) ...

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  10. Find the sum to n terms of each of the following series : n.1 + (n-1...

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  11. The sum of first P terms of an A.P. is equal to the sum of its first Q...

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  12. A series is given in the form : (1) + (2+3+4) + (5+6+7+8+9) +…. Find t...

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  13. The first and last terms of an A.P. are a and l respectively. If S be ...

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  14. If the first, second and last terms of A.P. be a, b, and c respectivel...

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  15. If S(n) be the sum of n consecutive terms of an A.P. show that, S(n+...

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  16. If S(n) be the sum of n consecutive terms of an A.P. show that, S(n+...

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  17. Let a(n) denote the n-th term of an A.P. and p and q be two positive i...

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  18. Find the sum of the three-digited natural numbers which leave a remain...

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  19. Between the roots of the quadratic equation 3px^(2) - 10px + 5q = 0 (p...

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  20. Let a(n) be the nth term of an A.P. and a(3) + a(5) + a(8) + a(14) + a...

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