माना हम निम्नलिखित श्रेणी का योग निकालना चाहते हैं-
This series has common ratio 2/3. If we multiply through by this common ratio, then the initial 1 becomes a 2/3, the 2/3 becomes a 4/9, and so on:
This new series is the same as the original, except that the first term is missing. Subtracting the new series (2/3)"s" from the original series "s" cancels every term in the original but the first,
A similar technique can be used to evaluate any self-similar expression.

योग
गुणोत्तर श्रेणी और सर्वनिष्ट अनुपात
उदाहरण
अभिसार का प्रमाण