广义Fibonacci数列的若干恒等式

Some Identities Concerning Generalized Fibonacci Sequence

研究广义Fibonacci数的求和公式,运用其递推关系和性质,推得n∑i=1b2iFi、∑ni=1biFi2、n∑i=1biFi3等的求和公式,得到一些新的恒等式。

The summation formula of generalized Fibonacci sequence was studied. Based on its recurrence re-lationship and some relevant properties, summation formulas, such as ^n∑i=1b^2iFi、^n∑i=1b^iF^2i、^n∑i=1b^iF^3i,etc. , are deduced, thereby some new identical equations are proved.