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define un 135 2n 1 you may recall that...

Question: define un 135 2n 1 you may recall that...

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Define Un :- 1.3.5.... (2n -1) You may recall that n! Select all statements below which give a correct justification of the monotonic behaviour of the sequences (yn)%1 and (2n)1

We have n+1 2n 1 n 4(n +1)2 SO nin- is strictly increasing. We have Un+1 2n 1 n 4(n 1)2 SO (Un )n-1 is strictly decreasing We have ynt1 (2n +2) (2n +1) 2n+1

We have (2n +2) (2n +1) 2n+1 2n +2 yn+1 < 1, 4(n+ 1)?_ = SO gn ) n=1 is strictly decreasing. We have 2n+1 (2n 1) (2n 2) 2n 2 > 1 2n(2n) (2n + 1) 2n So is strictly decreasing. We have

We have n+1 (2n +1) (2n2) 2n 2 -= >1, Zn (2n)(2n+1) 2n SO Zn )n=1 is strictly increasing. We have n+1 2n 2 2n 2n +1 S 1 SO is strictly increasing We have Un+i 2n +1

is strictly increasing We have Un+1 2n 1 n+ 1 1 yn SO (3n)n-1 is strictly increasing. We have n+1 2n + 2 2n 2n +1 <1, So n= is strictly decreasing

diverges O We have 3 +sin(n) 4 + cos(n) for all n eN, so that 3 sin (n) 4 +cos(n) Therefore the series 03sin(n) 4+cos(n) diverges. None of the other answers are corr ect.

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