Harvard Entrance Exams || No Calculator Allowed 📵

Harvard Entrance Exams || No Calculator Allowed 📵 #maths #algebra #mathematics

[@srinivasch-re2oq]

If we know value of Log8 then we can solve very easily without any calculator with simple multiplications. Every person who attends such exams will prepare to know Log1 to Log20 values, so that most of the problems can be solved.

[@walterwen2975]

Harvard Entrance Exams: 8⁵ + 8⁴ + 8³ + 8² + 8¹ + 8⁰ =? (8⁵ + 8⁴) + (8³ + 8²) + (8¹ + 8⁰) = 8⁴(8 + 1) + 8²(8 + 1) + (8 + 1) = (9)(8⁴ + 8²) + 9 8⁴ + 8² = 8²(8² + 1) = (64)(65) = (60 + 4)(60 + 5) = 3600 + 9(60) + 20 = 4160 8⁵ + 8⁴ + 8³ + 8² + 8¹ + 8⁰ = (9)(8⁴ + 8²) + 9 = (10 - 1)(4160) + 9 = 41600 - 4151 = 37449

[@guyhoghton399]

Sum of a G.P. : a(rⁿ - 1)/(r - 1) a = First term = 1 r = common ratio = 8 n = number of terms 1.(8⁶ - 1)/(8 - 1) = (2¹⁸ - 1)/7 = 37,449

[@JeremyDixon1968]

It's 1001001001001001 in base 2 Easy.