In the finite series \(\sum_{n=1}^{5} a_n\), what does the symbol \(n\) represent?

State whether \(\sum_{k=1}^{8} k^2\) is a finite series or an infinite series.

Expand \(\sum_{n=2}^{5} n\) without evaluating it first.

Write the first four terms of \(\sum_{j=0}^{\infty} (j+1)^2\).

Evaluate \(\sum_{n=1}^{4} 2n\).

Evaluate \(\sum_{m=0}^{3} 3^m\).

For \(a_n=5-n\), write \(\sum_{n=1}^{4}a_n\) as an ordinary sum and evaluate it.

A physics model adds four sample readings \(r_i=0.2i\) for \(i=1,2,3,4\). Write the total using sigma notation and evaluate it.

Expand and simplify \(\sum_{n=1}^{4}(n^2-n)\).

Write \(5+8+11+14+17\) using sigma notation with lower limit \(n=0\).

Explain why \(\sum_{n=1}^{3} n^2\) and \(\sum_{j=1}^{3} j^2\) have the same value, then evaluate it.

A learner says \(\sum_{n=1}^{\infty} a_n\) is the same object as the sequence \(a_1,a_2,a_3,\ldots\). Correct the statement.

Convert \(\sum_{n=3}^{6}(2n-1)\) into a sum that starts at \(k=0\), and check by expanding both forms.

Find a sigma notation for the finite sum \(\frac12+\frac13+\frac14+\frac15\) using an index that starts at \(n=1\).

For \(\sum_{n=p}^{p+3} n\), expand the series and simplify the result in terms of \(p\).

For which integer values of \(q\) does \(\sum_{n=2}^{q} n\) have exactly five terms?

The sum \(\sum_{n=0}^{N} (4-n)\) is expanded as \(4+3+2+1\). Find \(N\) and justify your answer.

Diagnose the error: \(\sum_{n=1}^{4}2^n=1+2+4+8\). Give the correct expansion and value.

Show that \(\sum_{n=1}^{N} c\) equals \(Nc\) for any constant term \(c\).

A student rewrites \(\sum_{n=1}^{4} n^2\) as \(\sum_{n=2}^{5} n^2\) because both sums have four terms. Explain why this is invalid and give the two values.