# Sum the series: 1x3+2x4+3x5+4x6+...+9999x10001+10000x10002

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### 2 Answers

1x3+2x4+3x5+4x6+...+9999x10001+10000x10002

The nth term of this series can be written as;

`T_n = n(n+2) = n^2+2n`

If the sum of the series is `S_n`

`S_n `

= `sum_(n=1)^10000n(n+2)`

= `sum_(n=1)^10000(2n)`

= 1/6(2*10000^3+3*10000^2+10000)+1/2*10000*10001

`= 3.334xx10^11`

**Therefore sum of the series is `3.334xx10^11`**

N term series is: Tn = n(n+2) = n^2+2n & the sum is:limits n=1 to n=1000(2n)

1/6(2*10000^3+3*10000^2+10000)+1/2*10000*10001

3.334*10^11