An Interesting Pattern

Algebra Level pending

Consider the following pattern: 

Row 1          1 + 2 = 3
Row 2          4 + 5 + 6 = 7 + 8
Row 3          9 + 10 + 11 + 12 = 13 + 14 + 15

Find the sum of either side of the equation for row 100

South African Mathematics Olympiad Problem 10 Junior Round 3 Paper 2010


The answer is 1015050.

Mark Mottian by Mark Mottian , 22, South Africa

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1 solution

Alex Zhong
Apr 10, 2015

sum of either side of nth row: S = n 2 + n 2 + 1 + ⋯ + n 2 + n = n ( n + 1 ) ( 2 n + 1 ) 2 . S=n^2+n^2+1+\cdots+n^2+n=\dfrac{n(n+1)(2n+1)}{2}.

n = 100 ⟹ S = 100 × 101 × 201 2 = 1015050 . n=100 \implies S=\dfrac{100\times 101 \times 201}{2}=\boxed{1015050}.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Great job!

Mark Mottian - 6 years, 2 months ago

Can you please help me how you develop this expression for series, I am very begineer and novice to this subject

Syed Baqir - 6 years, 1 month ago

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