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(1)/(1.2.3) + (1)/(2.3.4) + (1)/(3.4.5)+...

`(1)/(1.2.3) + (1)/(2.3.4) + (1)/(3.4.5)+ ..+(1)/(n(n+1)(n+2)) = (n(n+3))/(4(n+1)(n+2))`

लिखित उत्तर

Verified by Experts

The correct Answer is:
` = ((k+1)(k+4))/(4(k +2)(k +3))`
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SCIENCE PUBLICATION-गणितीय आगमन का सिद्धांत -प्रश्नावली 4.1
  1. 1.2.3 + 2.3.4+...+n(n + 1)(n + 2) = (n(n+1)(n + 2)(n+3))/(4)

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  2. 1.3 + 2.3^(2) + 3.3^(2) + ..+n.3^(n) = (2n -1)3^(n + 1) + (3)/(4)

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  3. 1.2 + 2.3 + 3.4+..+n(n+1)= [(n(n+1)(n+2))/(3)]

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  4. 1.3 + 3.5 + 5.7+..+(2n -1)(2n +1) = (n(4n^(2) + 6n -1))/(3)

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  5. 1.2 + 2.2^(2) + 3.2^(3)+..+n.2^(n) = (n -1)2^(n + 1) + 2

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  6. 1/2 + 1/4 + 1/8+..+1/(2^(n)) = 1 - 1/(2^(n))

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  7. (1)/(2.5) +(1)/(5.8)+(1)/(8.11)+..+(1)/(3n -1)(3n + 2) = (n)/(6n + 4)

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  8. (1)/(1.2.3) + (1)/(2.3.4) + (1)/(3.4.5)+ ..+(1)/(n(n+1)(n+2)) = (n(n+3...

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  9. a + ar + ar^(2) + ...+ ar^(n-1) = (a(r^(n) -1))/(r-1)

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  10. (1 + 3/1)(1 + 5/4)(1 + 7/9)...(1 + (2n +1)/(n^(2))) = ( n+1)^(2)

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  11. (1 + 1/1)(1 + 1/2)(1 + 1/3)..(1 + 1/n) = (n+ 1)

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  12. 1^(2) + 3^(2) + 5^(2) + ..+ (2n -1)^(2) = (n(2n -1)(2n +1))/(3)

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  13. (1)/(1.4) + (1)/(4.7) + (1)/(7.10)+ ..+(1)/(3n -2)(3n + 1) = (n)/(3n +...

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  14. (1)/(3.5) + (1)/(5.7) + (1)/(7.9) + ..+ (1)/(2n + 1)(2n + 3) = (n)/(3(...

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  15. 1 + 2 + 3+..+ n lt (1)/(8)(2n + 1)^(2)

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  16. n(n+1)(n+5), 3 का गुणज हैं।

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  17. 10^(2n -1) + 1, संख्या 11 से भाजय हैं।

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  18. x^(2n) - y^(2n),(x + y) से भाजय हैं।

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  19. 3^(2n + 2) - 8n -9 संख्या 8 से भाजय हैं।

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  20. 41^(n) - 14^(n) संख्या 27 का एक गुणज है।

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