Home
Class 11
MATHS
Prove that sum(r=0)^n 3^r n Cundersetr =...

Prove that `sum_(r=0)^n 3^r n` `Cundersetr` = `4^n`.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    NCERT BANGLISH|Exercise EXERCISE 8.2|12 Videos

  • BINOMIAL THEOREM

    NCERT BANGLISH|Exercise Miscellanous exercise on chapter 8|10 Videos

  • BINOMIAL THEOREM

    NCERT BANGLISH|Exercise Miscellanous exercise on chapter 8|10 Videos

  • APPENDIX 2 MATHEMATICAL MODELLING

    NCERT BANGLISH|Exercise EXAMPLE|2 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISES ON CHAPTER 24|1 Videos

Similar Questions

Explore conceptually related problems

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

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)^ssum_(s=1)^n^n C_s^s C_r=3^n-1.

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)= 2n.""^(4n-1)C_(2n-1) .

Prove that sum_(r=1)^(k) (-3)^(r-1) (3n)^C_(2r-1) = 0 , where k = 3n//2 and n is an even integer.

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

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) ""^(n)C_(r).(n-r)cos((2rpi)/(n)) = - n.2^(n-1).cos^(n)'(pi)/(n) .

prove that sum_(r=0)^n(-1)^r^n C_r . [ 1/(2^r)+(3^r)/(2^(2r))+(7^r)/(2^(3r))+(15^r)/(2^(4r))+ ......up to m terms ] = (2^(m n)-1)/(2^(m n)(2^n-1))