Use Gauss's approach to find a formula for the sum of the even numbers from 2 to 2n:
2 + 4 + 6 + ... + 2n
Your formula will be an expression involving n.

sum = n (n+1)

Step-by-step explanation:

Let S = sum

Gauss's approach

S = 2     + 4        + 6    + ...  + 2n -4  + 2n-2  +  2n

S = 2n + 2n-2 + 2n-4  +  ... +  6         + 4         + 2

add both equations term by term in order

2S = 2n+2  +  2n+2  + 2n+2 (n times

therefore

S = n(n+1)

check:

n = 1,  S = 1(1+1) = 2   [= 2]

n = 2,  S = 2(2+1) = 6   [= 2+4]

...

checks

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step-by-step explanation:

step-by-step explanation:

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