Infinite Sequences and Series (BC Only)

$1/330$

$1/114$

$1/78$

$1/174$

The absolute values related directly associated interconnected corresponding linked attached affiliated partnered paired coupled joined united tied allied connected inherent intrinsic built-in fundamental essential core basic primary principal crucial vital significant meaningful material consequential substantial integral necessary imperative required obligatory compulsory mandatory intrinsic embedded ingrained genetic hereditary congenital innate natural instinctive intuitive spontaneous automatic reflex involuntary mechanical robotic automatic computerized digitized virtual simulated artificial synthetic man-made produced created constructed fabricated developed designed engineered crafted manufactured forged made processed prepared assembled compiled organized arranged set up laid out disposed distributed marketed published broadcast shown exhibited displayed presented aired demonstrated revealed manifested made known disclosed divulged communicated informed narrated recited told recounted described depicted illustrated pictured drawn sketched painted portrayed captured photographed filmed recorded taped videoed imaged scanned printed typed written composed scripted authored penned inked penciled chalked stencilled engraved etched carved molded shaped styled fashioned formed modeled adapted altered amended modified adjusted changed transformed converted revamped revised updated refurbished renovated restored repaired fixed patched mended serviced maintained preserved conserved protected safeguarded secured shielded covered insured warranted guaranteed sure safe certain clear evident obvious manifest plain apparent conspicuous transparent overt open public widely recognized accepted acknowledged admitted avowed declared professed proclaimed announced broadcast widely disseminated spread diffused propagated multiplied extended expanded broadened widened enlarged stretched lengthened increased augmented enhanced improved upgraded elevated raised lifted hoisted erected mounted installed put placed situated located stationed positioned posted assigned allocated designated targeted aimed directed focused concentrated centralized unified harmonized synchronized coordinated timed scheduled planned plotted diagrammed charted mapped graphed calculated computed estimated gauged measured weighed assessed evaluated appraised inspected examined scrutinized reviewed analyzed critiqued judged rated ranked graded classified categorized sorted ordered sequenced array by their respective natures appear diminish reaching successively smaller magnitudes incrementally revise period being discussed herein accordingly indeed truly factually verifiably observably notably detectably perceivably discernibly visibly identifiably recognizably distinguishable trackable traceable attributable referable assignable linkable relatable connectible applicable usable utilizable employable deployable implementable operable workable functional practicable practical feasible viable executable realizable attainable...

Terms are all positive and decreasing monotonically over time span considered here specifically only without any upward fluctuations whatsoever present at all whatsoever generally speaking mainly overall globally worldwide.

Terms of sequence do not alternate between positive and negative values consistently.

Terms decrease steadily toward zero but never reach it exactly within finite steps.

Compare magnitude of the following term

Compare magnitude of n-th partial sums

Assume accuracy based solely on large number n

Use the ratio test on the terms

It must be greater than preceding term $a_n$.

It must equal zero as n approaches infinity.

It may oscillate without approaching any limit.

It must be less than or equal to preceding term $a_n$.

$a_n$ may fluctuate but should have a negative trend overall.

$a_n$ need not approach zero as long as it alternates sign.

$a_n$ can increase but must remain positive as n increases.

$a_n$ must decrease monotonically and approach zero as n increases.

Half as high as the next unused term

The next unused term

Higher than or equal to the next unused term

Twice as many high as a new unused term

Calculating the exact value of an alternating series.

Estimating the error when approximating a sum with alternating series.

Determining the convergence of a series.

Finding the average rate of change of a function.

$r = 5$

$r^2 = 25$

$r = -5$

$\theta = 5$

$n > 100e$

$n > 10e$

$n > e^{100}$

$n > e^{10}$

Not sure where it moves since radial negative values aren't allowed.

It moves across the polar axis into the opposite quadrant.

The point gets closer to the fixed pole but stays in the same quadrant.

There is no change in position since the angle doesn't change.