Home
Class 11
MATHS
Prove that sum(r=0)^n^n Crsinr xcos(n-r)...

Prove that `sum_(r=0)^n^n C_rsinr xcos(n-r)x=2^(n-1)sin(n x)dot`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

Prove that sum_(r=0)^n^n C_r3^r=4^n

Prove that sum_(r=0)^n3^r^n C_r=4^n .

Prove that sum_(r=0)^(n) ""^(n)C_(r )sin rx. cos (n-r)x = 2^(n-1) xx sin nx .

Prove that sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)

Prove that sum_(r = 0)^n r^3 . C_r = n^2 (n +3).2^(n-3)

Prove that sum_(r=0)^ssum_(s=1)^n^n C_s^n C_r=3^n-1.

Prove that sum_(r=0)^n r(n-r)(^nC_ r)^2=n^2(^(2n-2)C_n)dot

Prove that sum_(r=0)^(n) 3^( r" "n)C_(r ) =4^(n) .

If x + y = 1 , prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r) = nx .

Prove that sum_(r=0)^(2n)(r. ^(2n)C_r)^2=n^(4n)C_(2n) .

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Prove that sum(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n Cr=1/n .

    Text Solution

    |

  2. Prove that (C1)/1-(C2)/2+(C3)/3-(C4)/4++((-1)^(n-1))/n Cn=1+1/2+1/3++1...

    Text Solution

    |

  3. Prove that sum(r=0)^n^n Crsinr xcos(n-r)x=2^(n-1)sin(n x)dot

    Text Solution

    |

  4. Find the last two digits of the number (23)^(14)dot

    Text Solution

    |

  5. Find the last two digits of the number 27^(27)dot

    Text Solution

    |

  6. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

    Text Solution

    |

  7. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

    Text Solution

    |

  8. Using binomial theorem (without using the formula for .^n Cr) , prove ...

    Text Solution

    |

  9. Prove that .(r+1)*^n Cr-r*^n Cr+ ... +(-1)^r.^n Cr=(-1)^r.^(n-2)Crdot

    Text Solution

    |

  10. Find the sum .^n C0+^n C4+^n C8 + . . .

    Text Solution

    |

  11. Find the value of ^4nC0+^(4n)C4+^(4n)C8++""^(4n)C(4n) .

    Text Solution

    |

  12. Find the coefficient of x^n in the polynomial (x+^n C0)(x+3^n C1)xx(x+...

    Text Solution

    |

  13. If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the value of C2+2C...

    Text Solution

    |

  14. Prove that (.^n C0)/1+(.^n C2)/3+(.^n C4)/5+(.^n C6)/7+ . . . =(2^n)/(...

    Text Solution

    |

  15. Find the sum sumsum(0lt=ilt=jlt=n)^n Ci^n Cj

    Text Solution

    |

  16. Find the sum sumsum(i!=j)^n ^nCi^n Cj

    Text Solution

    |

  17. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as ...

    Text Solution

    |

  18. Prove that (1^2)/3""^n C1+(1^2+2^2)/5^n C2(1^1+2^2+3^2)/7^n C3+ +(1^2+...

    Text Solution

    |

  19. Prove that 1/(n+1)=(.^n C1)/2-(2(.^n C2))/3+(3(.^n C3))/4- . . . +(-1^...

    Text Solution

    |

  20. Find the sum 2C0+(2^3)/2C1+(2^3)/3C2+(2^4)/4C3++(2^(11))/(11)C(10)dot

    Text Solution

    |