Newton's Infinite GP Convergent Series Discovered By Nilakanta Somayaji

Evam yasthuthya ccheda paramabhaaga paramaparyayaa

ananthaayaa api samyoga: thasya ananthaanaam api kalpyamaanasya

yogasyaaddhyaavayavina:

parasparama cchedaad ekonacchedaa mamsa saadhyam

sarvathraapi samaanam eva…

  Thus the sum of an infinite series, whose later terms (after the first) are got by diminishing the preceding or by the same divisor, is always equal to the first term divided by one less than the common mutual divisor.]]>

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