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Algebra

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22 Jan 2012 11:20:51 IST

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Mathematics

let S= {2⁰,2¹,2²,.........2¹⁰}. Consider all possible positive differences of elements of S. if M is the sum of all this differences ,then the sum of the digits of M is?

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prahlad kumar sharma

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22 Jan 2012 11:22:42 IST

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S={2^0 , 2^2,2^3..........2^10}

Bipin Dubey

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22 Jan 2012 22:24:55 IST

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2^0 will come in RHS of minus sign 10 times. Its contribution -(10)(2^0)

2^1 will come in RHS & LHS of minus sign 9 times & 1 time respectively. Contribution -(8)(2^1)

Similarly contribution of 2^2 is -(6)(2^2) and so on....

M = -(10)(2^0)-(8)(2^1)......+8(2^9)+10(2^10)

= 10(2^10 - 2^0) + 8(2^9 - 2^1) + 6(2^8 - 2^2) + 4(2^7 - 2^3) + 2(2^6 - 2^4)

= 10230 + 4080 + 1512 + 480 + 96 = 16398

Sum of digits of M is 1+6+3+9+8 = 27

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