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Show that (1 xx 2^(2) + 2 xx 3^(2) + ......

Show that `(1 xx 2^(2) + 2 xx 3^(2) + ... +n xx (n + 1)^(2))/(1^(2) xx 2 + 2^(2) xx 3+ ... + n^(2) xx (n + 1)) = (3n + 5)/(3n + 1)`

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NCERT TAMIL-SEQUENCES AND SERIES-Miscellaneous Exercise On Chapter 9
  1. If (a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0) then show that ...

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  2. Let S be the sum, P the product and R the sum of reciprocals of n term...

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  3. The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectiv...

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  4. If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in A.P., prove that a,...

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  5. If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n +...

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  6. If a and b are the roots of x^2 – 3x + p = 0 and c, d are roots of x^...

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  7. The ratio of the A.M. and G.M. of two positive numbers a and b, is m :...

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  8. If a, b, c are in A.P., b, c, d are in G.P. and 1/c,1/d,1/e are in A.P...

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  9. Find the sum of the following series up to n terms: (i) 5+55+555+......

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  10. Find the 20^(th) term of the series 2 xx 4 + 4 xx 6 + 6 xx 8 + ... + ...

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  11. Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +......

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  12. If S1, S2, S3 are the sum of first n natural numbers, their squares a...

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  13. Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/...

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  14. Show that (1 xx 2^(2) + 2 xx 3^(2) + ... +n xx (n + 1)^(2))/(1^(2) xx ...

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  15. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and ag...

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  16. Shamshad Ali buys a scootor for Rs 22000. He pays Rs 4000 cash and agr...

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  17. A person writes a letter to four of his friends. He asks each one of t...

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  18. A man deposited Rs 10000 in a bank at the rate of 5% simple interest a...

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  19. A manufacturer reckons that the value of a machine, which costs him Rs...

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  20. 150 workers were engaged to finish a piece of work in a certain number...

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