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This brings us to the next topic: what is meant by the convergence of a series? 2 Convergence of a series An infinite series S is defined as the sum of the terms in an infinite sequence t1 ; t2 ; . . ; tn . . ; t∞ . The sum of the first n terms of an infinite sequence is denoted by Sn. If S tends to a finite limit as n, the number of terms in the series, tends to ∞, then S is said to be a convergent series. ∞ There are a number of convergence tests that are formally used to determine whether a series is convergent or divergent.

Test tube 1 Test tube 2 20 890 21 090 20 700 390 4 526 750 4 572 007 4 481 490 90 517 At first glance, you might question the results obtained for test tube 2. You interpret the absolute difference in the minimum and maximum counts as the range of error possible, and that difference for test tube 2 is approximately 206 times the count difference calculated for test tube 1! You assume that the mean count is the true value of, or best approximation to, the actual stem cell count in the test tube solution, and you continue to do some number crunching.

53. 717×10−4. The shaded number dictates the number of digits that can be retained in the result. 72×10−4. 1065. 11, after rounding. Multiplication and division When multiplying or dividing two or more numbers, choose the operand that has the least number of significant digits. The number of significant digits in the computed result corresponds to the number of significant digits in the chosen operand from the above step. 374 535. The shaded number has the smallest number of significant digits and therefore governs the number of significant digits present in the result.