Summation notation and index changes

Build fluency with summation notation, finite series and index changes. Practise reading lower and upper limits, counting terms, distinguishing an index from an external variable and translating a list of terms into sigma notation. The problems also cover linearity, weighted sums, reversed indexing and sums over a restricted interval.

Progress from direct expansion to transformations that preserve exactly the same terms. Both single-select and multiselect questions include worked explanations, endpoint checks and diagnoses of common mistakes such as double-counting a boundary or squaring a sum term by term. Any power-sum formula needed is supplied. No infinite-series convergence or telescoping theory is required. Work with exact arithmetic and write the first and last terms when checking an index change.