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onjecture a formula for the following product
\n" ); document.write( "the product of the nth number when (1-(4/(2i-1)^2))=
\n" ); document.write( "LET PN =(1-(4/(1)^2))(1-(4/(3)^2))(1-(4/(5)^2))...(1-(4/(2n-1)^2)),when i=1.
\n" ); document.write( "WHAT DO YOU MEAN BY I=1...I THINK IT SHOULD BE JUST AS GIVEN IN RHS WITH I=N...FURTHER USE OF I IS NOT DESIRABLE IN THESE SUMS AS IT MAY BE MISTAKEN AS THE COMPLEX/IMAGINARY NUMBER I.ANY WAY LET US DO THE PROBLEM BY TACKLING THE GENERAL FORM ...............(1-(4/(2n-1)^2))
\n" ); document.write( "={((2N-1)^2-4)/((2n-1)^2)}
\n" ); document.write( "=(4N^2-4N+1-4)/(2n-1)^2
\n" ); document.write( "=(4N^2-4N-3)/(2N-1)^2
\n" ); document.write( "=(4N^2-6N+2N-3)/(2N-1)^2
\n" ); document.write( "={2N(2N-3)+1(2N-3)}/(2N-1)^2
\n" ); document.write( "=(2N-3)(2N+1)/(2N-1)^2
\n" ); document.write( "HENCE THE REQUIRED PRODUCT PN IS OBTAINED BY PUTTING N=1,2,3....ETC..TILL N IN THIS.
\n" ); document.write( "PN= ((-1)*3/1^2)(1*5/3^2)(3*7/5^2)..{(2N-5)(2N-1)/(2N-3)^2}{(2N-3)(2N+1)/(2N-1)^2}
\n" ); document.write( "WE FIND ALL EXCEPT THE FOLLOWING CANCEL OUT..SO
\n" ); document.write( "PN=(-1)(2N+1)/(2N-1)^2 \n" ); document.write( "