SOLUTION: 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 inclu

SOLUTION: For what values of n does the product (13)(35)(57)(79)...((2n-1)(2n+1)) equal a perfect square? List out the first 5 values of n that will result in a perfect square and inclu

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.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
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.
LET PN=(1*3)(3*5)(5*7)(7*9)...((2n-1)(2n+1)).....PRODUCT UP TO N TERMS
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..
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
3^2=9....THAT IS 2N+1=9...OR...N=4
5^2=25....THAT IS 2N+1=25...OR...N=12
7^2=49....THAT IS 2N+1=49...OR...N=24
9^2=81....THAT IS 2N+1=81...OR...N=40
11^2=121....THAT IS 2N+1=121...OR...N=60
ETC.......
RELATED QUESTIONS
Identify a possible explicit rule for the nth term of the sequence 1, 1/3, 1/5, 1/7, 1/9, (answered by Edwin McCravy,ikleyn)

What is the nth term of the arithmetic sequence? 7, 5, 3, 1, � A. �2n B. 7 � 2n... (answered by richwmiller)

What are the excluded values of n in the expression n+5/(8-n)(n+3) x n-9/2n-3? Thank... (answered by stanbon)

PLEASE HELP ME WITH THIS EQUATION!! What are the excluded values of n in the expression... (answered by edjones)

What is the sum of {{{ sum( (3 * 5^(n+1)/2^(2n)), n=8, 13)... (answered by greenestamps,Edwin McCravy)

For what values of n will the infinite series (2n-1)+(2n-1)^2+...+(2n-1)^i+... have a... (answered by ikleyn)

Please help with this questions, prove by induction that the formulas positive integral... (answered by ikleyn)

k= 1!+ 2! +3!.......+n! what is the no. of values of n for which k is a perfect... (answered by Edwin McCravy)