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integer 𝑘𝑘≥1, that 1+3+5+⋯+(2𝑘𝑘−1)=𝑘𝑘2. WTST 1+3+5+⋯+(2(𝑘𝑘+1)−1)=(𝑘𝑘+1)2 that is 1+3+5+⋯+(2𝑘𝑘+1)=(𝑘𝑘+1)2=𝑘𝑘2+2𝑘𝑘+1 LHS =1+3+5+⋯(2𝑘𝑘−1)+(2𝑘𝑘+1)=𝑘𝑘2+(2𝑘𝑘+1)= RHS. Therefore, 1+3+5+⋯+(2𝑛𝑛−1)=𝑛𝑛2 for all l integers n ≥ 1 Use mathematical induction to prove that for all integers n ≥ 1,