document.write( "Question 28688: For what values of n does the product (1*3)(3*5)(5*7)(7*9)...((2n-1)(2n+1)) equal a perfect square? List out the first 5 values of n that will result in a perfect square and include a formula in terms of n. \n" ); document.write( "

Algebra.Com's Answer #15623 by venugopalramana(3286) $\"\"$ $\"About$

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For what values of n does the product (1*3)(3*5)(5*7)(7*9)...((2n-1)(2n+1)) equal a perfect square? List out the first 5 values of n that will result in a perfect square and include a formula in terms of n.
\n" ); document.write( "LET PN=(1*3)(3*5)(5*7)(7*9)...((2n-1)(2n+1)).....PRODUCT UP TO N TERMS
\n" ); document.write( "WE FIND THERE ARE ALWAYS A PAIR OF NUMBERS BEING MULTIPLIED (THAT IS THEY ALWAYS FORM A PERFECT SQUARE)EXCEPT FOR THE FIRST NUMBER 1 WHICH IS ANY WAY A PERFECT SQUARE AND THE LAST NUMBER.HENCE THE KEY IS THAT LAST NUMBER BEING MULTIPLIED WITH SHALL BE A PERFECT SQUARE..
\n" ); document.write( "SO WE SHOULD HAVE 2N+1 AS A PERFECT SQUARE..THAT IS WE SHOULD END WITH AN ODD NUMBER AS A PERFECT SQUARE ...SO PN WILL BE A PERFECT SQUARE FOR ENDINGS WITH
\n" ); document.write( "3^2=9....THAT IS 2N+1=9...OR...N=4
\n" ); document.write( "5^2=25....THAT IS 2N+1=25...OR...N=12
\n" ); document.write( "7^2=49....THAT IS 2N+1=49...OR...N=24
\n" ); document.write( "9^2=81....THAT IS 2N+1=81...OR...N=40
\n" ); document.write( "11^2=121....THAT IS 2N+1=121...OR...N=60
\n" ); document.write( "ETC....... \n" ); document.write( "

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