Home
Class 12
MATHS
[sum(n=0)^(n)(-1)^(r)*C(r)[(1)/(2^(r))+(...

[sum_(n=0)^(n)(-1)^(r)*C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+(7^(r))/(2^(3r))+(15^(r))/(2^(4r))+..." mterms "]=],[[" (1) "(2^(mn)-1)/(2^(mn)(2^(n)-1))," (2) "(2^(mn)-1)/(2^(n)-1)],[" (3) "(2^(mn)+1)/(2^(n)+1)," (4) "(2^(mn)+1)/(2^(n)-1)]]

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that sum_(r=0)^(n)(-1)^(r)nC_(r)[(1)/(2^(r))+(3)/(2^(2r))+(7)/(2^(3r))+(15)/(2^(4r))+...up to mterms]=(2^(mn)-1)/(2^(mn)(2^(n)-1))

Show that sum_(r=0)^(n) (-1)^(r ). ""^(n)C_(r ) {(1)/(2^(r )) +(3^(r ))/(2^(2r)) +(7^(r ))/(2^(3r)) +…."upto m terms"}=(2^(mn)-1)/(2^(mn)(2^(n)-1))

If sum_(r=0)^(n) (-1)^(r ).""^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+(7^(r))/(2^(3r))+"……..""to m terms"] = k(1-1/(2^(mn))) , then k =

find the sum of the series 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 ]

sum_(r=0)^n(-1)^r .^n C_r[1/(2^r)+3/(2^(2r))+7/(2^(3r))+(15)/(2^(4r))+ .....mt e r m s]= (2^(m n)-1)/(2^(m n)(2^n-1))

sum_(r=0)^n(-1)^r^n C_r[1/(2^r)+3/(2^(2r))+7/(2^(3r))+(15)/(2^(4r))+ u ptomt e r m s]= (2^(m n)-1)/(2^(m n)(2^n-1))

Sigma_(r=0)^(n)(-1)^(r).^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+...up rarr mterms ]

If sum_(r=0)^(2n)(-1)^(r)(2n(C_(r))^(2)=alpha_(1), then sum_(r=0)^(2n)(-1)^(r)(r-2n)(2n(C_(r))^(2)=

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)