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Prove that ((2n+1)!)/(n !)=2^n{1. 3. 5 ....

Prove that `((2n+1)!)/(n !)=2^n{1. 3. 5 .........(2n-1)(2n+1)}`

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Prove that: ((2n)!)/(n !)={1. 3. 5..... (2n-1)}2^ndot

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Prove that : 1+2+3++n=(n(n+1))/2

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Prove that: \ ^(2n)C_n=(2^n[1. 3. 5 (2n-1)])/(n !)

Using mathematical induction, prove that (1)/(1.3.5) + (2)/(3.5.7) +….+(n)/((2n-1)( 2n+1) ( 2n+3)) =( n(n+1))/( 2(2n+1) (2n+3))

RD SHARMA ENGLISH-PERMUTATIONS-All Questions
  1. If (n+1)! =90[(n-1)!], fin d n

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  2. If (n+3)! =56[(n+1)! ] find n

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  3. Prove that ((2n+1)!)/(n !)=2^n{1. 3. 5 .........(2n-1)(2n+1)}

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  4. There are 3 candidates for a classical, 5 for a Mathematical,, and 4 ...

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  6. Find the number of 4 letter words, with or without meaning which can b...

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  7. Given 4 flags of different colours, how many different signals can be ...

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  8. Find the number of different signals that can be generated by arrangin...

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  9. How many words (with or without meaning) of three distinct letters of ...

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  10. Find the total number of ways of answering 5 objective type questions,...

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  11. How many three digit numbers can be formed without using the digits ...

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  12. How many numbers are there between 100 and 1000 consists such that ...

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  13. How many numbers are there between 100 and 1000 such that 7 is the ...

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  14. How any three digit odd numbers can be formed by using the digits 1...

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  15. How many 3-digit even number can be formed form the digits 1,2,3,4,5,6...

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  16. How many numbers of 3 digits can be formed with the digits 1,2,3,4,5 ...

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  17. Find the number of numbers of 5 digits than can be formed with the ...

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  18. How many 4-digit numbers are there when a digit may be repeated an ...

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  19. How many three letter words can be formed using a , b , c , d , e if R...

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  20. In how many ways 5 rings of different types can be worn in 4 fingers?

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