Chapter 12 Sequences and Series - 12.1 Define and Use Sequences and Series - 12.1 Exercises - Skill Practice - Page 799: 62

False. See a counterexample below.

This is false, because, for example, $(a_{1}+a_{2})^{2}=a_{1}^{2}+2a_{1}a_{2}+a_{2}^{2}\neq a_{1}^{2}+a_{2}^{2}$, (if neither term is zero) So, for a counterexample, take $n=2, k=2,a_{1}=1,a_{2}=2$ LHS = $1^{2}+2^{2}=1+4=5$ RHS = $(1+2)^{2}=3^{2}=9$ Since $LHS\neq RHS,$ the statement is false.