Home
Class 11
MATHS
Prove that sum(r=0)^n^n Cr(-1)^r[i+i^(2r...

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

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that sum_(r=0)^(n)r(n-r)C_(r)^(2)=n^(2)(^(2n-2)C_(n))

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

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

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

Ifn>2than sum_(r=0)^(n)(-1)^(r)(n-r)(n-r+1)C_(r)=(A)0(B)n(C)2^(n)(D)(n-1)2^(n)

sum_(r=0)^(n)((n-3r+1)^(n)C_(r))/((n-r+1)2^(r)) is equal to

sum_(r=0)^n((-1)^r*C_r)/((r+1)(r+2)(r+3))=1/(a(n+b)), then a+b is