Home
Class 11
MATHS
If((n),(r )) "denotes " ""^nCr then (...

If`((n),(r )) "denotes " ""^nC_r then `
(a) Evalutae : `2^(15)((30),(0))((30),(1))-2^(14)((30),(1))((29),(14))+2^(13)((30),(2))((28),(13)).......-((30),(15))((15),(0))`
( b) Prove that : `Sigma_(r=1)^(n) ((n-1),(n-r))((n),(r))=((2n-1),(n-1))` ( c) Prove that : `((n),(r))((r),(k))=((n),(k))((n-r),(r-k))`

Text Solution

Verified by Experts

The correct Answer is:
`((30),(15))`
Promotional Banner

Topper's Solved these Questions

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise EXERCISE (J-M)|20 Videos

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise EXERCISE (J-A)|6 Videos

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise EXERCISE (S-1)|11 Videos

  • SOLUTION AND PROPERTIES OF TRIANGLE

    ALLEN|Exercise All Questions|62 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    ALLEN|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

If ((n),(r)) denotes nC_r , then Evaluate 2^15((30),(0))((30),(15))-2^14((30),(1))((29),(14))+2^13 ((30),(2))((28),(13))...............-((30),(15))((15),(0))

Prove that ((n),(r))+2((n),(r-1))+((n),(r-2))=((n+2),(r))

Prove that : sum_(i=0)^r((n+i),(k))=((n+r+1),(k+1))-((n),(k+1))

Prove that n(n-1)(n-2) ...(n-r+1)=(n!)/((n-r)!).

Deduce that: sum_(r=0)^(n)*^(n)C_(r)(-1)^(n)(1)/((r+1)(r+2))=(1)/(n+2)

Prove that (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!) =((n+1)!)/(r!(n-r+1)!)

Prove that ((n-1)!)/((n-r-1)!)+r.((n-1)!)/((n-r)!)=(n!)/((n-r)!)

Prove that (3!)/(2(n+3))=sum_(r=0)^(n)(-1)^(r)((^nC_(r))/(r+3C_(r)))