What conjecture can you make about the sum of the first 35 positive even numbers?

Question

parthkohli · Answer

Do you have to find the sum of the first 35 positive even numbers?

h_hoff · Answer

I have to find 2 numbers that multiply together to equal the sum of the first 35 positive numbers

parthkohli · Answer

Ah, I see.

parthkohli · Answer

Exercise: Find the sum of the first $n$ positive even numbers.

Hint: It is an arithmetic progression with first term $2$, last term $2n$ and number of terms $n$.

h_hoff · Answer

Thank you

parthkohli · Answer

Did you figure it out?

anonymous · Answer

$$2+4 + 6 +\cdots + 70=\
2(1+2+3+ +\cdots +35)=\
$$

anonymous · Answer

Apply the formula
$$1+2+3+\cdots+n=\frac{n(n+1)}2
$$

anonymous · Answer

$$1+2+3+\cdots +35=\frac {35\times 36}2$$

anonymous · Answer

$$2(1+2+3+\cdots+ 35)= 35\times 36
$$