Mathematics, 11.03.2021 04:00 ponyolovezsosuk1074
Use mathematical induction to prove the statement is true for all positive integers n. 1^2 + 3^2 + 5^2 + ... + (2n-1)^2 = (n(2n-1)(2n+1))/3)
Answers: 1
.
:
, under the assumption that 
is true:![(1^{2}+2^{2}+3^{2}+...+k^{2}) + [2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](/tpl/images/1186/3827/e14f4.png)
![\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)}{3} +[2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](/tpl/images/1186/3827/41fa4.png)
![\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot [2\cdot (k+1)-1]^{2}}{3} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](/tpl/images/1186/3827/88cc3.png)
![(2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)](/tpl/images/1186/3827/9bdd1.png)
Another question on Mathematics
Mathematics, 21.06.2019 13:30
Which expression is factored form? x^2+14x+48 a) (x-8)(x-6) b) (x+6)(x-8) c) (x+8)(x-6) d) (x+6)(x+8)
Answers: 1
Mathematics, 21.06.2019 15:30
Which of the following statements is not true? a.parallel lines are lines in the same plane that never intersect. b.congruent figures have the same shape and same size angles and sides. c.similar figures must have the same shape and the same size. d.a rotation is when you turn a figure around a certain point.
Answers: 1
You know the right answer?
Use mathematical induction to prove the statement is true for all positive integers n. 1^2 + 3^2 + 5...
Questions
Mathematics, 06.05.2020 06:35
Mathematics, 06.05.2020 06:35
English, 06.05.2020 06:35
Mathematics, 06.05.2020 06:35
Chemistry, 06.05.2020 06:35
Social Studies, 06.05.2020 06:35
English, 06.05.2020 06:35
Mathematics, 06.05.2020 06:35
Physics, 06.05.2020 06:35
Mathematics, 06.05.2020 06:35
