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Calculate the sum sum_n=05 n(n+1)

May 10, 2026Mathematics

ScanSolve AI Answer

Answer

70

3 steps

Here's how to solve the summation:

Expand the term inside the summation.
The expression is $n(n+1)$ .
$n(n+1) = n^2 + n$
Calculate each term for $n$ from 0 to 5.
For $n=0: 0(0+1) = 0 \times 1 = 0$
For $n=1: 1(1+1) = 1 \times 2 = 2$
For $n=2: 2(2+1) = 2 \times 3 = 6$
For $n=3: 3(3+1) = 3 \times 4 = 12$
For $n=4: 4(4+1) = 4 \times 5 = 20$
For $n=5: 5(5+1) = 5 \times 6 = 30$
Sum all the calculated terms.
$\sum_{n=0}^{5} n(n+1) = 0 + 2 + 6 + 12 + 20 + 30$ $= 70$
The sum is 70.

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