Solve
Sums and products
Integer ranges, written as expressions. 5 examples.
sum(body, i, a, b) and product visit each integer from a through b. If a is past b, the sum is 0 and the product is 1. A bound that is not a whole number is rejected. More than 100000 trips is a calculation error. A for range, including a downward step, is on the Loops page. Old does not run these. Interpreter and Compiler do.
The Basel problem
Eight thousand terms. The missing tail is about 1/n, and the gap is that size.
Machin's formula for π
Twenty terms of each arctangent. The gap against π is one unit in the last place.
Euler's constant
The 1/(2n) correction. At twenty thousand terms this is γ to about ten digits.
Wallis product
Forty factors. The product climbs toward π from below.
Euler product for ζ(2)
The first eight primes. What is missing is the rest of the primes, about one percent of π²/6.