1 + 4 + 9 + ... + n^2

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

(*View/Download .pdf file)

Adding Sequences in the Form: 12 + 22 +...+ n2:

   A.  This sequence can be solved by the following:

12 + 22 +...+ n2 = n(n+1)(2n+1)

                           6

1.  If one of the numbers is not divisible by 6, then one of the numbers will be divisible by 3 and another will divisible by 2.

2.  Simplify the expression.

3.  Multiply the remaining numbers.

Ex [1]  12 + 22 +...+ 102 =_________.

a)  According to the expression this simplifies to: 10(11)(21) / 6  which we can simplify to 5(11)(7) = 385.  See Multiplying By 11.

b)  The answer is 385.

Ex [2]  12 + 22 +...+ 122 =_________.

a)  According to the expression this simplifies to: (12)(13)(25) / 6 which we can simplify to 2(13)(25) = 26 x 25 = 650.  See Multiplying by 25.

b)  The answer is 650.

Ex [3]  1 + 4 + 9 +...+ 225 =_________.

a)  Notice this ends in 152.

b)  According to the expression this simplifies to: (15)(16)(31) / 6 which we can simplify to 5(8)(31) = 40 x 31 = 1240.

c)  The answer is 1240.

Back to top