Fractions, decimals & series
Add a long chain of fractions like 1/(1·2) + 1/(2·3) + …
Finding a common denominator across many terms is a wall of arithmetic — yet most of it cancels.
Spot it when
Denominators are consecutive products: 1·2, 2·3, 3·4… (a telescoping chain).
Watch it solved
Adding these directly means finding a common denominator. But the denominators are consecutive products — a pattern this sutra exploits.
A chain of fractions
Adding these directly means finding a common denominator. But the denominators are consecutive products — a pattern this sutra exploits.
⚡ Speed Advantage
See how few steps Vedic method needs!
When you’ll actually hit this
Real moments — exams, homework, competitions — where this shortcut earns its keep.
A series question in algebra hands you a four- or five-term fraction chain to total.
Each term splits into a difference; the middle pieces cancel, leaving 1 − 1/4 = 3/4.
A repayment series in commercial maths adds the same shape — you just need the closing total.
Only the ends survive: the sum is n/(n+1).
A quiz asks for the sum up to 1/(9·10) and rewards whoever answers first.
Telescopes to 1 − 1/10 = 9/10 instantly.
The method behind it
सोपान्त्यद्वयमन्त्यम्
Sopāntyadvayamantyam
“The ultimate and twice the penultimate”
In certain sum-of-fractions equations, the answer combines the last and second-to-last terms in a specific ratio.
LCM, addition of fractions — many steps.
pattern recognition on last two terms.
Use when
- • Equations matching the ultimate-penultimate pattern
Avoid when
- • General fraction addition