#recursive definitions

57 messages · Page 1 of 1 (latest)

marsh lynx
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dont get how to do 3d
first 5 terms are:
1, 5, 14, 30, 55

image.png
dull pivot
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Uh I haven’t done this before but what does it it mean by recursive definition?

median sandal
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I recognise d and c lol

marsh lynx
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like erm

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dont even know

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this is part of chapter 3 in edexcel yr 2 pure

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series and sequences

dull pivot
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U sub in r=1,2,3,4,5

marsh lynx
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yh ik

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and i got those terms above the pic

dull pivot
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Are they wrong?

marsh lynx
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dont think so

dull pivot
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So what part is confusing u

marsh lynx
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the recursive definition part

dull pivot
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oh then I can’t help u 😭

marsh lynx
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have u not covered it

dull pivot
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Not in my spec

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The definition part

marsh lynx
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edexcel?

dull pivot
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Never seen it before

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No I do aqua

marsh lynx
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oh

dull pivot
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Aqa*

marsh lynx
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calm

dull pivot
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I’ve done series but not q to do with definition

marsh lynx
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alr np

dull pivot
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Ohhh nvm

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I think it means

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Un+1=

marsh lynx
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yeah

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first you have to define the first term

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so u1 = 1 in this case

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then do the Un+1

foggy compass
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you can see from the jump from 30 to 55 theres probably only 1 U_n in it

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so if u take that off each term

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u have 4, 9, 16, 25

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so its U_n+1 = U_n + (n+1)^2

marsh lynx
light cradle
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If you do further maths then you should know that 1/6r(r+1)(2r+1) is the sum of the first r square numbers

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So its just u_n = 1² + 2² + 3² + ... + n²

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so u_{n+1} =

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u_{n} + (n+1)²

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If you don't do further maths then you just look at the first differences

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So you can just calculate u_{n+1} - u_{n} = 1/6(n+1)(n+2)(2n+3) - 1/6n(n+1)(2n+1) and expand and simplify to (n+1)²

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And you get the same result

harsh sequoia
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Didn’t u do this q yesterday?

marsh lynx
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yh

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i got it now tho

marsh lynx
light cradle
dull pivot
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I think u do

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For r^2

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And r^3

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Wait

light cradle
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Ye 1/4n²(n+1)²

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For cubes

dull pivot
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Yep