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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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` = (3n + 5)/(3n + 1)`
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NEW JOYTHI PUBLICATION-SEQUENCES AND SERIES -QUESTIONS FROM COMPETITIVE EXAMS
  1. Show that (1 xx 2^(2) + 2 xx 3^(2) + ... +n xx (n + 1)^(2))/(1^(2) xx ...

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  2. The sum to n terms of the series 1/2 + 3/4 + 7/8 + 15/16 + ....... is

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  3. 0.2 + 0.22 + 0.222 + …….. to n terms =

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  4. If (a^(n + 1) + b^(n + 1))/(a^(n) + b^(n)) is the arithmetic mean betw...

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  5. If (i)^(2) = -1, (i)^(2) + (i)^(4) + (i)^(6) + ...... to (2n + 1) term...

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  6. If S(n) denotes the sum of n terms of an A.P., S(n +3) - 3S(n + 2) + 3...

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  7. The HM of 2 numbers is 4. Their AM is A and GM is G. If G satisfies 2...

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  8. The angle of triangle are in 30^(@). The greatest angle in radians is

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  9. How many terms of the geometric series 1 + 4 + 16 + 64 + ……… will make...

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  10. Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the ...

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  11. The sum of the series 1 + 2.2 + 3.2^(2) + 4.2^(3) + 5.2^(4) + ……… + 1...

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  12. If A, G, H denote respectively the AM, GM and HM between two unequal p...

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  13. Let a, b, c be district real numbers. If a, b, c are in G.P and a + b ...

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  14. The numbers of terms of the A.P 3, 7, 11, 15, …… to be taken so that t...

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  15. If the progression 3, 10, 17, …… and 63, 65, 67, …… are such that thei...

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  16. Which term of the geometric sequence 5,2,4/5 , 8/(25) … is (128)/(15...

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  17. If a, b and c are respectively the p^(th),q^(th)and r^(th) terms of an...

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  18. The sum of infinite terms of the geometric progression (sqrt(2) + 1)/(...

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  19. The two geometric means between the numbers 1 and 64 are

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  20. If 1 + (1 + 2)/2 + (1 + 2 + 3)/3 + ...... to n terms is s, then s is e...

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  21. If a, b, and c are in A.P., then which one of thew following is not tr...

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