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2n*2+2*2^(2)+3*2^(3)+...+n*2^(n)=(n-1)2^...

2n*2+2*2^(2)+3*2^(3)+...+n*2^(n)=(n-1)2^(n+1)+2

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1*2+2*2^(2)+3*2^(3)+*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

1.2+2.2^(2)+3.2^(3)dots...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

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

1 ^(2) + 2^(2) + 3^(2) + . . . + n^(2) = (n (n + 1) (2 n + 1))/( 6)

P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N is true then 1^(2) +2^(2) +3^(2) + ........ + 10^(2) = .......

1+2.2+3.2^(2)+4.2^(3)+...+n*2^(n-1) = (i) 1+ (1+n) 2^(n) (ii) 1- (1+n) 2^(n) (iii) 1- (1-n) 2^(n) (iv) 1+ (1-n) 2^(n)

Prove that 1^(2)+2^(2)+3^(2)+.....+n^(2)=(n(n+1)(2n+1))/6