document.write( "Question 1028128: My uncle has 6 million dollars to spend.
\n" ); document.write( "On the first day he spent $1, on the second day he spent $2, on the third day he spent $4, and so forth with the amount doubling every day.
\n" ); document.write( "If he continues to spend every day, how long will his 6 million dollars last? \n" ); document.write( "

Algebra.Com's Answer #652326 by jorel555(1290) $\"\"$ $\"About$

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Let's use the first 4 days. Your uncle will have spent:
\n" ); document.write( "1+2+4+8=15
\n" ); document.write( "15+1=16=2^4
\n" ); document.write( "Similarly, for five days we have:
\n" ); document.write( "1+2+4+8+16=31
\n" ); document.write( "31+1=32=2^5
\n" ); document.write( "Generalizing, it is apparent that the sum of 2^0+2^1+2^2+....+2^n=2^n+1
\n" ); document.write( "If we want to spend 6 million dollars, then:
\n" ); document.write( "2^n+1=6000000
\n" ); document.write( "2^n=5999999
\n" ); document.write( "n, in this case, is somewhere between 2^22 and 2^23, so his money will last only until shortly after the 22nd day!!!!!!!!!!!!! \n" ); document.write( "

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