Home
Class 11
MATHS
Prove that sum(r=0)^n^n Cr(-1)^r[i^r+i^(...

Prove that `sum_(r=0)^n^n C_r(-1)^r[i^r+i^(2r)+i^(3r)+i^(4r)]=2^n+2^(n/2+1)cos(npi//4),w h e r ei=sqrt(-1)dot`

Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

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

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

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n C_r=1/n .

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

Prove that "^n C_r+^(n-1)C_r+...+^r C_r=^(n+1)C_(r+1) .

The value of sum_(r=0)^(3n-1)(-1)^r 6nC_(2r+1)3^r is

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

Prove that sum_(r=1)^(n) tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(-1) (2^(n)) - (pi)/(4)