Question

Can someone explain the steps 3 and 4 please? Thanks a lot <3

Answer 1

Please see below.

Explanation:

2.5

`= ([(2-1)(3-1)(4-1) * * * ((n-1)-1)(n-1)][(2+1)(3+1)(4+1) * * *((n-1)+1)(n+1)] )/([2*3*4* * * (n-1) * n][2*3*4* * * (n-1) * n])`

3.5

`= ((1)cancel(2)cancel(3) * * * cancel((n-2))cancel((n-1)))/(cancel(2)cancel(3)cancel(4)* * * cancel((n-1)) * n) * (cancel(3)cancel(4)cancel(5) * * * cancel((n))(n+1))/(2*cancel(3)cancel(4)cancel(5) * * * cancel((n-1)) cancel(n))`

Answer 2

To add more terms see below.Please carefully observe each term.

`1*2*3*4*5*6*...(n-2)(n-1)(n)(n+1)...etc`

Explanation:

First we take Step:`2`
`(color(red)((2-1))(2+1)color(red)((3-1))(3+1)color(red)((4-1))(4+1)...color(red)((n-1))(n+1))/(color(red)([2*3*4...(n-1)n])[2*3*4...(n-1)n]`

Separating red and black color

`=(color(red)((2-1)(3-1)(4-1)(5-1)...(n-1)))/(color(red)([2*3*4...(n-1)n]))xx((2+1)(3+1)(4+1)(5+1)...(n+1))/([2*3*4...(n-1)n]`

`=(color(red)(1*2*3*4*5...(n-1)))/(color(red)([2*3*4...(n-1)n]))xx(3*4*5*6*7...(n-1)n(n+1))/([2*3*4...(n-1)n])`

`=(1*color(red)(2*3*4*5...(n-1)))/((color(red)(2*3*4...(n-1)))n]xx(3*4*5*6*7...(n-1)ncolor(blue)((n+1)))/([color(blue)2*3*4...(n-1)n])`

`=1/nxx(n+1)/2`

`=(n+1)/(2n)`