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Show that (2n)!/n!=[1.3.5……………….(2n-1)]2...

Show that `(2n)!/n!=[1.3.5……………….(2n-1)]2^n`.

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Prove that : (2n) ! = 2^n (n!)[1.3.5.... (2n-1)] for all natural numbers n.

Show that S_(n)=(n(2n^(2)+9n+13))/(24) .

Show that the middle term in the expansion of (1+x)^(2n) is (1.3.5….(2n-1))/(n!) 2^(n)x^(n) , where n is a positive integer.

Prove that : ^(2n)C_n = (2^n [1.3.5. ..........(2n-1)])/(n!) .

Show that (1xx2^2+2xx3^2+....+nxx(n+1)^2)/(1^2xx2+2^2xx3+...+n^2xx(n+1))=(3n+5)/(3n+1) .

Show that ((n+1)(n+2)(n+3)...... (n+r))/(r!) is a whole number.

Use the principle of mathematical induction to show that 5^(2n+1)+3^(n+2).2^(n-1) divisible by 19 for all natural numbers n.

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If S_1,S_2,S_3 be the sum of n, 2n, 3n terms of a G.P., show that : S_1(S_3-S_2)= (S_2-S_1)^2 .

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JBD PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXAMPLE
  1. How many 3-digit numbers are there without repetition?

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  2. If 1/(6!)+1/(7!)=x/(8!), find x

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  3. Show that (2n)!/n!=[1.3.5……………….(2n-1)]2^n.

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  4. How many 4-digit numbers are there with no digit repeated?

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  5. How many numbers are there between 1000 and 9999 so that no digit is r...

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  6. In how many ways can 5 girls be seated in a row so that two girls Ridh...

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  7. In how many ways can 5 girls be seated in a row so that two girls Ridh...

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  8. Find the number of permutations of the letters of word 'DISSIMILAR' wh...

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  9. If nC6=nC2, find ^nC2.

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  10. If 10Cr=^10C2 find the values of r.

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  11. A bag contains 5 black and 6 red balls. Determine the number of ways i...

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  12. In how many ways can a student choose a programme of 5 courses if 9 co...

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  13. How many chords can be drawn through 21 points on a circle?

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  14. Out of 18 points in a plane, no three are in the same straight line ex...

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  15. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and ...

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  16. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and ...

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  17. If (n!)/(2!(n-2)!):(n!)/(4!(n-4)!) =2:1. Find the value of n.

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  18. show that 2^16 divides 32!. also, find the largest value of n for whic...

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  19. What is the largest power of 2 contained in 32!.

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  20. How many different words (with or without meaning) can be formed using...

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