then 9tm+1 is also triangular. Write each of the following numbers as the sum of three or fewer triangular numbers: 1 69, (b) (c) 185, (a) 56, (d) 287. 5. For n 1, establish the formula (2n+1)? 1 (4t,+1)-(4t,2 BUS 6 Verify that 1225 and 41,616 are simultaneously square and triangular numbers. [Hint: Finding an integer n such that g tinidmou bonincb of no n(n + 1) dutn 1225 2 ud is equivalent to solving the quadratic equation n2n- 2450 = 0.] *w 7. An oblong number counts the number of dots in a rectangular array having one more row than it has columns; the first few of these numbers are sln 01 2 02 6 03 12 04 =20 and in general, the nth oblong number is given by Оn n(n+1). Prove algebraically and geometrically that (а) On 2+4 6+ + 2n. Any oblong number is the sum of two equal 11 () : :

then 9tm+1 is also triangular. Write each of the following numbers as the sum of three or fewer triangular numbers: 1 69, (b) (c) 185, (a) 56, (d) 287. 5. For n 1, establish the formula (2n+1)? 1 (4t,+1)-(4t,2 BUS 6 Verify that 1225 and 41,616 are simultaneously square and triangular numbers. [Hint: Finding an integer n such that g tinidmou bonincb of no n(n + 1) dutn 1225 2 ud is equivalent to solving the quadratic equation n2n- 2450 = 0.] *w 7. An oblong number counts the number of dots in a rectangular array having one more row than it has columns; the first few of these numbers are sln 01 2 02 6 03 12 04 =20 and in general, the nth oblong number is given by Оn n(n+1). Prove algebraically and geometrically that (а) On 2+4 6+ + 2n. Any oblong number is the sum of two equal 11 () : :

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 91E

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