1^3 + 2^3 +...+ n^3

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: 13 + 23 + ... + n3:

   A.  A sequence in this form reduces to:

                                                         

   B.  Notice that this expression is the same thing as: (1 + 2 +...+ n)2

1.  Multiply the last number by that number plus 1, then divide by 2.

2.  Square this result.

Ex [1]  13 + 23 +...+ 103 =_________.

a)  Using the expression this reduces to: (10)(11) / 2 = 5 x 11 = 55.

b)  552 = 3025.  See Squaring A Number Ending In 5.

c)  The answer is 3025.

Ex [2]  13 + 23 +...+ 153 =_________.

a)  Using the expression this reduces to: (15)(16) / 2 = 15 x 8 = 120.

b)  1202 = 14400.

c)  The answer is 14400.

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