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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 1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 1+2+3+4+5+4+3+2+1
Based on the previous question, evaluate:
1+2+3+⋯+8+9+8+⋯+3+2+1. 1 + 2 + 3 + \dots + 8 + 9 + 8 + \dots + 3 + 2 + 1. 1+2+3+⋯+8+9+8+⋯+3+2+1.
From what you have learnt, which expression represents the sum
1+2+3+⋯+(n−1)+n+(n−1)+⋯+3+2+1? 1 + 2 + 3 + \dots + (n-1) + n + (n-1) + \dots + 3 + 2 + 1 ? 1+2+3+⋯+(n−1)+n+(n−1)+⋯+3+2+1?
Hence or otherwise, what is the value of the expression:
1+2+3+⋯+49+50+49+⋯+3+2+1? 1 + 2 + 3 + \dots + 49 + 50 + 49 + \dots + 3 + 2 + 1? 1+2+3+⋯+49+50+49+⋯+3+2+1?
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