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The sum sumsum_(0leilejle10) (""^(10)C_(j))(""^(j)C_(r-1))is equal to |
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Answer» `2^(10)- 1` `= .^(10)C_(1)(.^(1)C_(0) + .^(1)C_(1))+.^(10)C_(2)(.^(2)C_(0)+.^(2)C_(1) + .^(2)C_(2))+"...."+.^(10)C_(10)(.^(10)C_(0) +.^(10)C_(1)+"..."+.^(10)C_(10))` `= .^(10)C_(1)(2) + .^(10)C_(2)(2^(2))+.^(10)C_(3)(2^(3))+"....."+.^(10)C_(10)(2^(10))` `= (2+1)^(10) - 1` `= 3^(10) - 1` |
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