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#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

$ a_n=100+n^2.\,\, n=1,2,3,----$

$d_n=(a_n,a_{n+1})$

find :max($d_n)$

$d_n=(a_n,a_{n+1})$

find :max($d_n)$

- Thread starter Albert
- Start date

- Thread starter
- #1

- Jan 25, 2013

- 1,225

$ a_n=100+n^2.\,\, n=1,2,3,----$

$d_n=(a_n,a_{n+1})$

find :max($d_n)$

$d_n=(a_n,a_{n+1})$

find :max($d_n)$

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- Feb 7, 2012

- 2,725

$ a_n=100+n^2.\,\, n=1,2,3,----$

$d_n=(a_n,a_{n+1})$

find :max($d_n)$

- Mar 31, 2013

- 1,322

= (100+n^2 , 100 + n^2 + 2n + 1)

= (100+n^2, 2n + 1) subtracting 1st term from second

= ( 200+2n^2 , 2n + 1) doubling 1st as 2nd is odd

= (200+ 2n^2- n(2n+1), 2n+ 1)

= ( 200 - n , 2n + 1)

= (400- 2n ,2n + 1) doubling 1st as second is odd

= ( 400 -2 n + 2n+ 1,2n+1)

= (401,2n + 1)

it shows

1) cannot be > 401

2) is 401 when 2n +1 = odd multiple of 400

or 2n + 1 = 401(2k+ 1) = 802k + 401

or 2n = 802k + 400

or n = 401 k + 200

we are able to find n as well for which it is 401