Find the recurrence relation a(n) = a(n−1) + n with a(0) = 0

Question

enter preformatted text here find the recurrence relation.

a(n)=a(n−1)+n with a(0)=0

Do I have to make a replace? Can someone help with initial steps?

Thanks.

Do like this....

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Answer 1

$a_n = a_{n-1} + n=$

$a_{n-2}+ (n-1) + n=$

$a_{n-3} + (n-2) + (n-1) + n=$

.....

$ a_2 + 3 + 4...... + (n-2) + (n-1) + n=$

$a_1 + 2 + 3 + 4...... + (n-2) + (n-1) + n=$

$a_0 + 1 + 2+ 3 + 4...... + (n-2) + (n-1) + n=$

$0+1 + 2+ 3 + 4...... + (n-2) + (n-1) + n=$

$\frac {n(n+1)}2$.