Let S=2+4+6+…+2N, where N is the smallest positive integer such that S>1,000,000. Then the sum of the digits of N is:

1968 AMC 12 Problem 26

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26.

Let

S=2+4+6+\cdots+2N,

where

N

is the smallest positive integer such that

S\gt1{,}000{,}000.

Then the sum of the digits of

N

is:

27

12

6

2

1

The sum is

N(N+1)

Compare

999\cdot1000

and

1000\cdot1001

with one million

We have

S=N(N+1).

For

N=999,

this is

999{,}000\lt1{,}000{,}000,

while for

N=1000

it is

1{,}001{,}000.

Thus

N=1000,

whose digit sum is

1.

Therefore, the correct answer is E.