Either development. Determine n so the tenth term of the development to be the biggest.

[mystic mantle]

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[tame tartan]

So T 9+1 is the biggest

[terse vault]

Hm, interesting.
Well, first of all, what's the tenth term?

[tame tartan]

i can use the formula

[terse vault]

Yeah, you can use the binomial expansion.

[tame tartan]

yea

[terse vault]

Yeah, that's correct. Though, I'm not 100% sure what to do next.

[tame tartan]

yea me neither

[terse vault]

Let's call it a(n).

Try calculating a(n + 1)/a(n).

[tame tartan]

yea

like this formula

[terse vault]

Wait, what's x?

We don't have an x here.

[tame tartan]

is a formula for this case

[terse vault]

Oh, you meant the general case, ok.

[tame tartan]

yea mb

[obtuse olive]

The current price of Bitcoin is $51,061.90, if it drops to 39000$ and if a person invest PKR 5,000 in Bitcoin, and later it reaches $100,000, what will be his profit in rupees?"

The current price of Bitcoin is $51,061.90, and if a person invest PKR 5,000 in Bitcoin, and later it reaches $100,000, what will be his profit in rupees?"

1usd is = 278 pkr

[narrow raptor]

saad.anwar09
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[terse vault]

Don't invade other people's threads. Make your own.

[obtuse olive]

sorryy my bad

[tame tartan]

oh wow and i was thinking that somebody will help us

:)))

[obtuse olive]

im sorry for invading ur thread

[terse vault]

You can't use this formula here, as the term in the binomial also depends on n.

We need to do it explicitly.

a(n) = C(n, 9) 2^(n - 9) n^9
a(n + 1) = C(n + 1, 9) 2^(n - 8) (n + 1)^9
As C(n + 1, 9)/C(n, 9) = (n + 1)/(n - 8), we get:
a(n + 1)/a(n) = 2(n + 1)^10/(n^9 (n - 8))

Now, we need to find the maximum value of that expression.

We can do that as usual, by differentiation.

[tame tartan]

how can we use differentiation?

we know tho that the tenth term is the biggest

how can we use that

[terse vault]

Well, we find the derivative of 2(n + 1)^10/(n^9 (n - 8)) with respect to n.

[tame tartan]

i do not really understand how we can use a derivative here

[terse vault]

As usual: quotient and product rules.

[tame tartan]

so i just derivate this?

[terse vault]

Differentiate. And yes.

[tame tartan]

is 0?

[terse vault]

Well, we need to set it to be equal to 0.

The derivative obviously isn't just 0, though.

[tame tartan]

yea