Basic Mathematics

# Pyramid Counting Warmup

How many circles are in the final group?

Using the pattern above as an aid, evaluate the sum:

$1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1$

Based on the previous question, evaluate:

$1 + 2 + 3 + \dots + 8 + 9 + 8 + \dots + 3 + 2 + 1.$

From what you have learnt, which expression represents the sum

$1 + 2 + 3 + \dots + (n-1) + n + (n-1) + \dots + 3 + 2 + 1 ?$

Hence or otherwise, what is the value of the expression:

$1 + 2 + 3 + \dots + 49 + 50 + 49 + \dots + 3 + 2 + 1?$

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