Nathan

(1) ln(1+x)= Σ-1^(n+1) * x^n / n

where the sum goes from k = 1 to infinity.

This is a well-known fact that can be easily derived. However, why is the following sum also valid?

(2) ln(1+x) = Σ x^k / (1+x)^k / k

where the sum goes from k = 1 to infinity and |x| / |x+1| < 1

I was wondering how to show this. You don't need to show all the steps. I was just wondering why this is true, as it doesn't seem trivial to go from (1) to (2).

Aghanim is a boss from a link to the past. To beat him you need to 6 red throws.

The first throw is red

The second throw is red/blue with 50% chance

The third throw is red/blue with 50% chance

The fourth throw is red/blue with 50% chance

The fifth throw is lightning

The sixth throw is red

The seventh throw is red/blue with 50% chance

...

This continues until you get 6 red throws (it's a cycle of 5).

WHAT is the probability of getting 0,1,2,...15 blue ball throws?

P(0) = 0.5^4 = 0.0625

P(1) = ??

P(2) = ??

...

How do you show that:

sum(x =1 to infinity) x*r^x = r/(1-r)^2

For the following identities:

d = 1 - v

i - d = id

I am supposed to give a verbal explanation for why they are correct, not just show that they are correct mathematically. Any ideas?

I was wondering whether this website:

http://www.businessnewsdaily.com/

is reliable for using as a source for a paragraph that I have to write. I was wondering whether there are easy ways to tell if such a source is reliable or not.

Let V be a finite dimension vector space with Basic B = {v1, ... vn}. Let w1,.... wn be n vector in vector space W. Suppose that T1 and T2 are two linear transformations from V to W such that T1(vi) = T2(vi) = wi for 1 <= 1 <= n. Prove that T1 = T2.