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Per NCERT, the proof of Sₙ = n(n+1)/2 uses the algebraic identity 2S = n(n+1). What is the geometric INSIGHT behind this?
AAll sums equal 0
BTriangles always have area 1
CNumbers cancel out
DTwo copies of the staircase 1+2+...+n fit together to form a rectangle of dimensions n × (n+1) — so 2S equals n(n+1)
Answer & Solution
Correct answer: D. Two copies of the staircase 1+2+...+n fit together to form a rectangle of dimensions n × (n+1) — so 2S equals n(n+1)
Per NCERT §8.5 Fig 8.5, the rectangular array of n×(n+1) circles is formed by two copies of the staircase — proving 2S = n(n+1).
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