Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 10 + 20 + 30 + . . . + 10n = 5n(n + 1)
What will be an ideal response?
| S1: | 10  (5 ? 1)(1 + 1) |
5 ? 210 = 10 ?
Sk: 10 + 20 + 30 + . . . + 10k = 5k(k + 1)
Sk+1: 10 + 20 + 30 + . . . + 10(k + 1) = 5(k + 1)(k + 2)
We work with Sk. Because we assume that Sk is true, we add the next multiple of 10, namely
10(k+1), to both sides.
10 + 20 + 30 + . . . + 10k + 10(k + 1) = 5k(k + 1) + 10(k + 1)
10 + 20 + 30 + . . . + 10(k + 1) = (k + 1)(5k + 10)
10 + 20 + 30 + . . . + 10(k + 1) = 5(k + 1)(k + 2)
We have shown that if we assume that Sk is true, and we add 10(k+1) to both sides of Sk, then Sk+1 is also true. By the principle of mathematical induction, the statement Sn is true for every positive integer n.
Mathematics
You might also like to view...
Determine the quotient.
A. 30 B. Undefined C. 1 D. 0
Mathematics
Find an equation for the graph.
A. y = 2 cos (4x)
B. y = 2 cos 
C. y = 4 cos (2x)
D. y = 4 cos 
Mathematics
Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.R = $2500, i = 6.9% interest compounded quarterly for 
A. $288,108.08 B. $98,572.66 C. $280,764.88 D. $433,035.61
Mathematics
Factor the binomial completely.9 - x2y2
A. (3 - xy)(3 + xy) B. (3 - xy)2 C. (3 + xy)2 D. prime
Mathematics