#### Document Type

Article

#### Publication Date

2010

#### Abstract

Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined by r1(x) =: ∑∞ n=0 anx n , r2(x) =: ∑∞ n=0 bnx n and r3(x) =: ∑∞ n=0 cnx n (here each ri(x) is a certain rational function in x), then a 3 n + b 3 n − c 3 n = (−1)n , ∀ n ≥ 0. Motivated by this amazing identity, we state and prove a more general identity involving eleven sequences, the new identity being ”more general” in the sense that equality holds not just for the power 3 (as in Ramanujan’s identity), but for each power j, 1 ≤ j ≤ 5.

#### Publication Title

The Fibonacci Quarterly

#### Publisher

Canadian Mathematical Society and Dalhousie University

#### Volume

48

#### Issue

1

#### First Page

34

#### Last Page

38

#### Recommended Citation

McLaughlin, J.
(2010).
An Identity Motivated by an Amazing Identity of Ramanujan.
*The Fibonacci Quarterly, 48*(1), 34-38.
Retrieved from https://digitalcommons.wcupa.edu/math_facpub/50

## Comments

Preprint version is available here.