Use mathematical induction to prove that each of the given statements is true fo

Question

Use mathematical induction to prove that each of the given statements is true for every positive integer n. 1 / 5 + 1 / 25 + 1 / 125 + + 1 / 5n = 1 / 4 - 1 / 4 middot 5n When n = 1, both sides of the equation are equal to ; thus the statement is true. Assume that the statement is true for n = k. Then 1 / 5 + 1 / 25 + 1 / 125 + + 1 / 5k = Add 1 / 5k+1 to both sides of the equation to get Thus, the statement is for n = k + 1. Therefore, by the Principle of Mathematical Induction, the statement is for all positive integers n.

Explanation / Answer

a)1/5 b)1/4 -1/(4*5^k) c)4

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.