What is the sum of the first 31 positive odd integers?

Question

Not really sure what this means

Answer 1

Any odd integer can be written as 2n -1 where n is an integer.

The sum of the first 31 positive odd integers is

 

∑_n=1³¹(2n-1)

= 2∑_n=1³¹ n - ∑_n=1³¹ 1

=2(31)(32)/2 - 31

= 31(32-1)

= 961.

Answer 2

1+3+5+7+...+61 = 961   &nbsp: [this is 31 odd integers]

 

Now, the first 62 numbers (that is, twice 31) are 1..62.

 

Gauss's formula for the sum of the numbers from 1 to N is:   sum = N(N+1)/2

 

The sum of the numbers from 1 to 62 is sum=62*63/2 = 1953.

In computing that sum, we included 2+4+6+...+62,

      which is 2*(1+2+3+...+31) = 2*31*32/2 = 992

 

Subtracting the sum of the even numbers,

       1953 - 992 = 961

Answer 3

1+3+5+7+...+31=256.

 

Odd are integers that are not divisible by2.

 

There is a formula for calculating that sum.