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Let N=(2+1)(2^(2)+1)(2^(4)+1)......(2^(3...

Let `N=(2+1)(2^(2)+1)(2^(4)+1)......(2^(32)+1)+1and n2^(lamda)"then the value of" lamdais `

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Let N=(2+1)(2^(2)+1)(2^(4)+1).........(2^(32)+1)+1 and N=2^(lambda) then the value of lambda is

1+2.2+3.2^(2)+4.2^(3)+......+n.2^(n-1)

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is

Let S_(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+......+(1)/(2^(n)-1) Then

1.2+2.2^(2)+3.2^(3)+....+n.2^(n)=(n-1)2^(n-1)+2

1.2+2.2^(2)+3.2^(3)+....+n.2^(n)=(n-1)2^(n-1)+2

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/(2))*k^(2) , then S_(n) can take value

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/(2))*k^(2) , then S_(n) can take value