Find the sum to 10 terms of the series `1xx2+2xx3+ 3xx4+ 4xx5+......`

Options

A. 400
B. 440
C. 385
D. None of these

Answer

B

Explanation

`1xx2+2xx3+ 3xx4+ 4xx5+......+n(n+1)`

Here `n=10`

Now

`S_n=sum_(r=1)^(n) n(n+1)=n^2+n`

Then

`S_n= sum_(r=1)^(n) n^2+ sum_(r=1)^(n) n`

`S_n=(n(n+1)(2n+1))/6+(n(n+1))/2`

`S_n=(n(n+1))/2[(2n+1)/3+1]`

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