MATH SOLVE

4 months ago

Q:
# Proof by mathematical induction

Accepted Solution

A:

Answer:See below.Step-by-step explanation:I will assume that 3n is the last term.First let n = k, then:Sum ( k terms) = 7k^2 + 3kNow, the sum of k+1 terms = 7k^2 + 3k + (k+1) th term= 7k^2 + 3k + 14(k + 1) - 4= 7k^2 + 17k + 10 Now 7(k + 1)^2 = 7k^2 +14 k + 7 so 7k^2 + 17k + 10 = 7(k + 1)^2 + 3k + 3= 7(k + 1)^2 + 3(k + 1)Which is the formula for the Sum of k terms with the k replaced by k + 1.Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.But the formula is true for 1 term because 7(1)^2 + 3(1) = 10 . So it must also be true for all subsequent( 2,3 etc) terms.This completes the proof.