"आर्यभट" के अवतरणों में अंतर

37 बैट्स् नीकाले गए ,  2 वर्ष पहले
छो (बॉट: आंशिक वर्तनी सुधार।)
==== बीजगणित ====
''आर्यभटीय '' में आर्यभट ने [[वर्ग|वर्गों]] और [[घन|घनों]] की [[श्रृंखलाश्रेणी (गणित)|श्रृंखलाश्रेणी]] के सुरुचिपूर्णरोचक परिणाम प्रदान किये हैं।<ref>{{cite book|first=Carl B.| last=Boyer |authorlink=Carl Benjamin Boyer |title=A History of Mathematics |edition=Second |publisher=John Wiley & Sons, Inc. |year=1991 |isbn=0471543977 |page = 207 |chapter = The Mathematics of the Hindus |quote= He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes.}}</ref>
:<math>1^2 + 2^2 + \cdots + n^2 = {n(n + 1)(2n + 1) \over 6}</math>