Generalized Formulas for Summation and Alternating Summation of Jacobsthal and Jacobsthal – Lucas Numbers

Mirwais Mansoor Kakar

doi:10.62810/jnsr.v4i2.377

Authors

Mirwais Mansoor Kakar Ghazni University, Mathematics Department, Faculty of Education, Ghazni, Afghanistan

DOI:

https://doi.org/10.62810/jnsr.v4i2.377

Keywords:

Generalized alternating summation formula, Generalized summation formula, Jacobsthal numbers, Jacobsthal -Lucas numbers

Abstract

The study was conducted at Zonal Agricultural Research Station, University of Agricultural Sciences, GKVK, Bangalore, to assess the impact of various bio-stimulants on the biotic resistance, quality, and storage behavior of potato (Solanum tuberosum L.) during the Ll, 2022-23, and R, 2023. The experiment was designed as a randomized complete block design (RCBD) with nine treatments and three replications, using bio-stimulants such as humic acid, amino acids, seaweed extracts, and microbial consortia. The treatment combination of whole tubers + RDF + Humic acid at 2 mL L^-1 significantly enhanced plant resistance against pests and diseases. This treatment led to the lowest aphid and cutworm populations, reduced tuber moth infestation, and minimized the incidence of early blight, late blight, and bacterial wilt compared to the control—further, the same treatment combination improved tuber quality, viz., TSS and starch content. Additionally, it resulted in lower percentage of physiological loss of weight (PLW) and sprouting during storage under room temperature, with minimal tuber rot. In contrast, the control treatment recorded the highest pest populations, disease incidence and post-harvest losses. These findings suggest that the treatment comprising whole tubers, RDF, and Humic acid at 2 ml L^-1 effectively improves biotic resistance, quality, and storage behavior of potatoes under ambient conditions.

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