document.write( "Question 1197684: Compute the infinite sum of (-6/7)^k-1 \n" ); document.write( "

Algebra.Com's Answer #831059 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The statement of the problem is incomplete; we don't know the starting value of k.

\n" ); document.write( "The formula for the infinite sum of a geometric sequence is

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document.write( "        first term\r\n" );
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document.write( " 1 minus the common ratio

\n" ); document.write( "The common ratio is clear: (-6/7).

\n" ); document.write( "But the first term depends on the starting value of k.

\n" ); document.write( "If the starting value is k=1, then the first term is $\"%28-6%2F7%29%5E0=1\"$ , and the infinite sum is $\"1%2F%281-%28-6%2F7%29%29=1%2F%281%2B6%2F7%29=1%2F%2813%2F7%29=7%2F13\"$

\n" ); document.write( "But if the starting value is k=0, then the first term is $\"%28-6%2F7%29%5E%28-1%29=-7%2F6\"$ , and the first term is

\n" ); document.write( "And there is no reason the starting value couldn't be any other (positive or negative) integer.

\n" ); document.write( "ANSWER (maybe): 7/13

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