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Compute 1 + 2 + 3 +....+ 99 + 100 + 99 + 98 +...+ 3 + 2 + 1

User LittleO
by
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1 Answer

4 votes

Answer:

10000

Explanation:

When computing a consecutive sum of integers with a difference of 1.

Use gauss's formula of (n/2)(first number + last number).

with n being the # of integers.

Since it is ascending and descending, it can be broken down into 2 sequences:

1 + 2 + 3 + ... + 99 and 1 + 2 + 3 + ... + 100.

Once each is calculated, add them up to find the value.

So:

1 + 2 + 3 + ... + 99 = (99/2)(100) = 4950.

1 + 2 + 3 + ... + 100 = (100/2)(101) = 5050.

4950 + 5050 = 10000

User Phil Mok
by
8.1k points

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