1 + 3 + 5 + ... + 2n-1

Home 1 + 2 + ... + n 1 + 3 + 5 + ... + 2n-1 a+(a+b)+...+(a+nb) 1 + 4 + 9 + ... + n^2 1^3 + 2^3 +...+ n^3 1^3 - 2^3 + 3^3 -...+ n^3 Add Decreasing Series Sub Decreasing Series Add Infinite Series Finding The Next Term Finding The nth Term Add Factorials

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Adding a sequence in the form: 1 + 3 + ... + 2n-1:

   A.  A sequence in this form reduces to:

1 + 3 + 5 + ... + 2n - 1 = (number of terms)2

   B.  To find the number of terms easily just add 1 to the last number and divide by 2.

Ex [1]  1 + 3 + 5 + ... + 21 =_________.

a)  Find the number of terms: (21 + 1) / 2 = 11.

b) 112 = 121. 

c)  The answer is 121.

Ex [2]  1 + 3 + 5 + ... + 205 =_________.

a)  Find the number of terms: (205 + 1) / 2 = 103.

b)  1032 = 10909.  See Multiplying Numbers Greater Than 100.

c)  The answer is 10909.

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