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Tuesday, September 16, 2008

Q) Find the sum of 1 + (1+2) + (1+2+4) +....... till n terms .

A)
1 + (1+2) + (1+2+4) + ...... till n terms

= 1 + [1*(2^2 -1)/(2-1)] + [1*(2^3 - 1)/(2 - 1)] + ....(1 + 2 + 4 + ...2^(n-1) ) ---->( Concept of sum of infinite Geometric Progression )

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

= 1 + [2^2 - 1 + 2^3 - 1 + 2^4 - 1 .... + 2^n - 1]

= 1 + [ 2^2.(2^(n-1) - 1) / (2-1) - (n-1) ]

= 1 + [ 4. 2^(n-1) - 4 - n + 1]

= 2^(n+1) - 2 - n

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