Solution Found!
Let a be a real number. Use induction to prove that Pni=0(a+i) = 12 (n+1)(2a+n) for
Chapter 4, Problem 16(choose chapter or problem)
QUESTION:
Let a be a real number. Use induction to prove that \(\sum_{i=0}^{n}(a+i)=\frac{1}{2}(n+1)(2 a+n)\) for every nonnegative integer n.
Questions & Answers
QUESTION:
Let a be a real number. Use induction to prove that \(\sum_{i=0}^{n}(a+i)=\frac{1}{2}(n+1)(2 a+n)\) for every nonnegative integer n.
ANSWER:Step 1 of 4
Consider the given statement,
\(P(n): \sum_{i=0}^{n}(a+i)=\frac{1}{2}(n+1)(2 a+n)\)
Check for P(1) as,
\(\begin{array}{l} \sum_{i=0}^{1}(a+i)=\frac{1}{2}(1+1)(2 a+1) \\ (a+0)+(a+1)=\frac{1}{2}(1)(2 a+1) \\ 2 a+1=2 a+1 \end{array}\)
Thus, it is observed that P(1) is true.