In English, a sequence is an ordered collection of numbers defined by a function on some set composed of natural numbers.The question is: "Find 3 properties of this sequence:"
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I find that all the number in this sequence is odd.
(1) What other properties this sequence have?
(2) Can I use the word "series" instead of "sequence"?
I suspect that they want attributes of the given sequence, not an altered sequence.If you (all the readers) are finding more thing you can write.
Here are some conclusions:
(1)*If the series had 3 members that are consequent they will be once odd and once even alternately.
(2)*The sum of two number
with different parity (even and odd sum) the sum will be odd
and:
if the sum of two number
with the same parity ((even and even sum) or (odd and odd sum) will be even
(3)*If the middle member of 3 consequent members is even the sum is even (i.e., 1+2+3=6) and:
if the middle member is odd the sum is odd (i.e. 2+3+4=9);
(4)*The difference between the series (sequence results) is equal to the number of member of the sequence.
Now, what you, the reader, can add?!
Note number three is unclear to me.I suspect that they want attributes of the given sequence, not an altered sequence.
(1) Each member of the sequence is odd. (You already found that one.)
(2) Each member + 2 equals the next member.
(3) The partial sum Sn formed from the sequence equals what?
Simply means "the sum of the FIRST n terms".(3) The partial sum Sn formed from the sequence equals what?
Not only are the terms all odd numbers but the terms are ALL the odd numbers (in order)The question is: "Find 3 properties of this sequence:"
View attachment 10615
I find that all the number in this sequence is odd.
(1) What other properties this sequence have?
(2) Can I use the word "series" instead of "sequence"?
The first numbers in each sum are the non-negative integers, 0, 1, 2, …, in that order. The second numbers are one more than the first. It seems obvious to me that this is n+ (n+1)= 2n+ 1.
After "2" is "3" so after 2+ 3= 5 should be 3+ 4= 7 and then 4+ 5= 9.