Question

URGENT VA ROG
radical din 1+2^0+2^1+2^2+.........+2^28+2^29
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Answer 1

$a = 1 + {2}^{0} + {2}^{1} + {2}^{2} + ... + {2}^{28} + {2}^{29}$

$2a = 2 + {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{29} + {2}^{30}$

$2a - a = 2 + {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{29} + {2}^{30} - 1 - {2}^{0} - {2}^{1} - {2}^{2} - ... - {2}^{28} - {2}^{29}$

$a = 2 + {2}^{30} - 1 - 1 = 2 + {2}^{30} - 2 = {2}^{30}$

$\sqrt{a} = \sqrt{{2}^{30} } = \sqrt{ {( {2}^{15} )}^{2} } = {2}^{15}$