1) In a ballroom dance competition, each couple is identified by a number worn on the leader's back. At a recent competition, forty couples competed. Their numbers are listed below: 109 111 118 122 123 128 132 136 145 153 160 165 171 176 182 184 188 190 193 199 202 205 210 213 217 222 230 233 236 243 248 252 255 258 264 270 273 276 281 287 Dances at the competition are organi

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Q: hat is the number of partitions of 2n into exactly n parts?

A: The number of partitions of 2n into exactly n parts:

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.