Question

Show that the sum of the first 2n natural numbers is n(2n+1).

Answer 1

I figured it out, let me type it out

Answer 2

hurry up

Answer 3

The sum of natural numbers can be considered as

\(\text{1+2+3+4+5...}\)

We can indicate that as

\(\sum_{n=0}^{∞} n+1\)

It is asking for the sum of the first 2n natural numbers, so it is asking for us to prove

\(\sum_{n=0}^{2n} n+1 = n(2n+1)\)

By the general formula for the sum of an arithmetic series, which is \(S_{n}=\frac{n}{2}\left(2a+\left(n-1\right)d\right)\), we can now substitute the values from \(\sum_{n=0}^{2n} n+1\)

\(\left(S_{2n}=\frac{2n}{2}\left(2\left(1\right)\right)+\left(2n-1\right)\left(1\right)\right)\)

Simplified, that is \(S_{2n}=n\left(2+2n-1\right)=n\left(2n+1\right)\)



Hence, we have proved that
\(\sum_{n=0}^{2n}n+1=n\left(2n+1\right)\)

Answer 4

Do you understand this now?

Answer 5

no your dumb

Answer 6

\(\color{#0cbb34}{\text{Originally Posted by}}\) @PapiChulo
no your dumb
\(\color{#0cbb34}{\text{End of Quote}}\)
The fact you can't use *your and you're* correctly makes you the dumber one buddy

Answer 7

\(\color{#0cbb34}{\text{Originally Posted by}}\) @PapiChulo
no your dumb
\(\color{#0cbb34}{\text{End of Quote}}\)

He wasted his precious time on answering your question with out a flaw and gave you an explanation and this is what you have to say..shameful.