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Q: Does 2n plus 1 equal 107?

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That factors to (2n + 1)(n + 2)

(4n + 1)*(2n + 6) = 8n2 + 26n + 6

Any even number can be written in the form 2n for some natural number n.Any odd number can be written as 2n+1 for a natural number nNow add an even to an odd.2n+2n+1=4n+1 which is 2(2n)+1 and this is the form for an odd number.

The sum of the numbers given is 31. 1 + 2 + 4 + 8 + ... + 2n = 2n+1 - 1

aneuploidy

If: 2n = 1 Then: n = 1/2 or 0.5

1 + 2 + 4 + ... + 2n = 2n+1 - 1

6=(1-2n)+5 6-5=(1-2n)+5-5 1=1-2n 1-1=1-1-2n 0=-2n 0/-2=-2n/-2 0=n

1

5n + 1 = 10 + 2n5n - 2n + 1 - 1 = 10 - 1 + 2n - 2n3n = 93n/3 = 9/3n = 3

41.

use mathematicl induction to show that (5/4/4n+1)powerox1/2< or equal(1.3.5....(2n+1)/2.4.6.....(2n)< or equal(3/4/2n+1)power of 1/2

The nth odd number is equal to 2n - 1. In this instance, 2 x 20 - 1 = 39.

Not much more than any other series like this. If you stop at the nth position the sume so far is n2. Because (n+1)2 is n2 + (2n+1), and 2n+1 are the odd numbers.

108

the answer is 0

n = 1

1/2n + 1/(2n+2) = 1/2*[(1/n + 1/(n+1)] = 1/2*(2n+1)/[n*(n+1)] or (2n+1)/[2*n*(n+1)]

2n2 + 15n + 7 = 2n2 + n + 14n + 7 = (2n2 + n) + (14n + 7) = n(2n + 1) + 7(2n + 1) = (2n + 1)(n + 7)

n(2n - 1)(2n + 7)

This question can be expressed algebraically as: (1/n) + (1/(2n)) + 2 = 23, (1/n) + (1/(2n)) =21, ((1+2)/(2n)) = 21, (3/(2n)) = 21, or 2n = (3/21), 2n = (1/7), so n = (1/14). This, by the way, is an elementary algebraic proof that the solution to the above relation is (1/14). Anyway, to answer the question, reread the question: "[What integer is such that] the reciprocal of the integer...". notice, the reciprocal of (1/14) is 14, which is the integer in question! ^_^

(2n)2 + (2n+1)2 = 4n2 + 4n2 + 2n + 2n + 1 = 8n2 + 8n + 1 = 8(n2 + n) + 1 Anything multiplied by 8 will be even. Add 1 makes it odd. Mark Ravenwood Folkestone School for Girls

12+4n = 2n12+4n-4n = 2n-4n12 = -2n-1/2(12 = -2n)-6 = n

2n + 1 = 22 Take 1 from the left side of the equal side and move it to the right side. To do this subtract 1 from the left side and on the right side 2n + 1 - 1 = 22 -1 2n = 21 Then divide both sides by 2 in order to isolate n. 2n / 2 = 21 /2 n = 21/2 or 10.5 Tada! The answer is 21/2 or 10.5.

1st term= 3 2nd term = 5 Nth term = 2n+1 10th term= 21 = 2(10)+1