help

[indigo parrot]

Idk what I'm doing

[unreal marten]

well part a

just plug in r=4 r=5 r=6

and you should see it looks a lot like a geometric series

then you can use the sum to infinity of a geometric series

which is in the formula booklet

the second part first rewrite it using log laws

and plug in n=1 n=2 ect and see what happens or if there's a pattern

[indigo parrot]

Oh hmm alr ill have a go

Idk where to find the answers tho 💔🫠

[frigid frost]

you take fm right?

the last part is pretty much just method of differences

since you can see that every term will cancel apart from the log_5(50) and the -log_5(2)

[scenic sorrel]

split up logs use methods of differences which is year 2 further maths

[quartz compass]

This is a normal maths question

[quartz compass]

$$\log_5 (\frac{3}{2}) , \log_5 (\frac{4}{3}) , \log_5 (\frac{5}{4})$$

[open tangle]

penaldo3142

[quartz compass]

Those are you first few terms

You see both the numerator and denominator increase by 1 each time

And you can use the log rule that adding a log of the same base you can multiply the arguments

$$\log_5 (\frac{3456...50}{2345...49})$$

[open tangle]

penaldo3142

[indigo parrot]

Omg guys I'm just seeing this my bad 💔😭 thank u so much for the help I'll go over this

[indigo parrot]

No 💔

[quartz compass]

And everything will cancel but and the 50 on the numerator and 2 on the denominator

[frozen elbow]

you can take the log 5 out

not as a constant

but u can still

[indigo parrot]

Oh whaa then why is my teacher giving me these questions-

[indigo parrot]

Ohkayy

[frozen elbow]

you can rewrite it as,
log_5 [sigma thing] (n+2/n+1)

[indigo parrot]

Ohhhhhhh righttt

[quartz compass]

So in the end you get

$$\log_5 (\frac{50}{2})$$

[open tangle]

penaldo3142

[quartz compass]

Which is 2

[indigo parrot]

Ohhh I seeee

OKAY I rlly appreciate itt

Thank uu