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Prove that: (1)/((1+a)(2+a)) + (1)/((2+a...

Prove that: `(1)/((1+a)(2+a)) + (1)/((2+a)(3+a))+ (1)/((3+a)(4+a)) + …..oo=(1)/(1+ a)`

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By using the principle of mathematical induction , prove the follwing : P(n) : (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …….+ (1)/(n(n+1)) = (n)/(n+1) , n in N

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KUMAR PRAKASHAN-SEQUENCE AND SERIES-Solutions of NCERT Exemplar Problems -Question of Module
  1. Prove that: (1)/((1+a)(2+a)) + (1)/((2+a)(3+a))+ (1)/((3+a)(4+a)) + …....

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  2. The terms 1,1,2,3,5,8,13,……respresents which sequence?

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  3. Which is the sequence whose terms are not finite?

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  4. What does a(1) + a(2) + a(3) + …..+ a(n) represent

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  5. Give new series by adding 2 in each term of arithmetic sequence 2,4,6,...

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  6. Find twelveth term of A.P. 4, 8, 12…….

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  7. 3 + 6+ 9 +…….Find sum of n terms.

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  8. 4 + 8 + 12+…….Find sum of first 15 terms.

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  9. Obtain arithmetic mean of 2 and 128

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  10. Insert 5 arithmetic mean between 3 and 4.

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  11. Find 8^(th) term of geometric sequence 3, 6,12,….

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  12. Find n^(th) term of Geometric sequence 1,3,9,27,……

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  13. Find S(n) for geometric sequence 4, 8, 15, 32,……

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  14. Find sum of first 10 terms of geometric series 3,9, 27,……

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  15. Find geometric mean of numbers 5 and 125.

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  16. Insert 3 geometric mean between 4 and 64.

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  17. The arithmetic and geometric mean of two positive numbers are 8 and 4 ...

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  18. If A and G be A.M. and G.M., respectively between two positive numbers...

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  19. Find value : 5^(2) + 6^(2) + 7^(2)+ …….+ 25^(2)

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  20. Prove the following by using the principle of mathematical induction f...

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