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Maths Functions, Limits, Continuity and Differentiability General Subjective Type

Published on: August 14, 2026

If | f(p + q) – f(q)| ≤ for all p and q ∈ Q & q ≠ 0, show that

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| f(2 k ) – f(2 i )| = | f(2 k ) – f(2 k –1 ) + f(2 k–1 ) – f(2 k–2 )......... f(2 i+1 ) – f(2 i )|

≤ | f(2 k ) – f(2 k–1 )| + | f(2 k–1 ) – f(2 k–2 )| + ...........| f(2 i+1 ) – f(2 i )|

Consider | f(2 k–1 + 2 k–1 )| – f(2 k–1 ) | ≤ 1

So | f(2 k ) – f(2 i )| ≤ 1 + 1 + ........(k – i) term ≤

≤ ≤ Hence proved.

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