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Show that C1^2 + 2C2^2 + 3C3^2 + ... + "...

Show that `C_1^2 + 2C_2^2 + 3C_3^2 + ... + "^nC_n^2` = `((2n-1!))/{(n-1)!}^2`

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Show that C_1^2 + 2C_2^2 + 3(3^2 + ... + "^nC_n^2 = ((2n-1!))/{(n-1)!}^2

Show that: C_1^2+2C_2^2+3C_3^2...+nC_n^2=frac[(2n-1)!][{(n-1)!}^2

Show that C_2 + 2C_3 + 3C_4 + ... + (n-1)C_n = 1+ (n-2) 2^(n-1)

Show that C_0 C_1 + C_1 C_2 + C_2 C_3 + .... + C_(n-1) C_n = (2n!)/((n-1)!(n+1!))

Find the sum of C_1 + 2C_2 + 3C_3 + .... + nC_n

Show that C_0 + 3C_1 + 5C_2 + .... +(2n+1) C_n = (n+1)(2^n)

Show that C_0 n^2 + C_1 (2-n)^2 + C_2 (4-n)^2 + .... + C_n (2n-n)^2 = n.2^n

Prove that "^(2n)C_0 + ^(2n)C_2 + .... + ^(2n)C_(2n) = 2^(2n-1)

Prove that "^(2n)C_1 + ^(2n)C_3 + .... + ^(2n)C_(2n-1) = 2^(2n-1)

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MODERN PUBLICATION-SAMPLE PAPER 2015-EXERCISE
  1. Prove that the measure of the angle between two main diagonals of a cu...

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  2. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  3. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  6. Solve the following equations by cramer's rule : 7x+y+1 = 0, x+13y+5 =...

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  7. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  8. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  9. How many four digits even numbers with distict digits can be formed ou...

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  10. In how many ways can 10 boys and 10 girls sit in a row so that no two ...

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  11. Find the fifth term in the expansion of (6x-a^3/x)^10

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  12. Two different digits are selected at random from the digits 1 through ...

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  13. Suppose that the probability that your alarm goes off in the morning i...

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  14. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  15. Evaluate intfrac[dx][cosx(1+2sinx)]

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  16. If vec a = 2 hat i + hat j, vec b = - hat i + 2 hat k, vec c = 2 hat i...

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  17. A sphere of constant radius k passes through the origin and meets the ...

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  18. Maximize z=-10x+2y Subject to -x+yge-1 ,x+yle6 ,yle5, x,yge0

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  19. Show that C1^2 + 2C2^2 + 3C3^2 + ... + "^nCn^2 = ((2n-1!))/{(n-1)!}^2

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  20. From a box containing 32 bulbs out of which 8 are defective 4 bulbs ar...

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