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The value of the expression (sum(r=0)^1...

The value of the expression `(sum_(r=0)^10 "^10 C_r)(sum_(k=0)^10 (-1)^k (^10 C_k)/2^k)` is :

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The sum of the series sum_(r=0)^(10) .^(20)C_(r) , is 2^(19)+{(.^(20)C_(10))/2} .

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