document.write( "Question 1061883: 1-(1/4)+(1/9)-(1/16)+(1/25)-............=?
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Algebra.Com's Answer #676648 by rothauserc(4718) $\"\"$ $\"About$

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1-(1/4)+(1/9)-(1/16)+(1/25)-............=?
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\n" ); document.write( "we can rewrite this as
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\n" ); document.write( "summation i=1,...+infinity of (-1)^(i+1) / i^2
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\n" ); document.write( "The approach is to break the sum into even and odd parts
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\n" ); document.write( "we know that summation i=1,...+infinity of 1/i^2 = pi^2/6
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\n" ); document.write( "The even part is (1/2)^2 + (1/4)^2 plus (1/6)^2, etc. Factoring out (1/4) shows that this even part sum is one fourth of the total sum. So, the odd part is 3/4 of the sum. 3/4 - 1/4 is a half, so the series converges to pi^2 / 12
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