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MatildaMatildaMatil... What is the 1000th letter?
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What's the greatest number of sides a polygon on a dotty grid could have?
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The picture illustrates the sum 1 + 2 + 3 + 4 = (4 × 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
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Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
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Put the steps of this proof in order to find the formula for the sum of an arithmetic sequence
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Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
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This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
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Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
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Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
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A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
