Hi I hope someone can help me with this problem: Prove the following formula by induction: 1+(1/2)+(1/4)+(1/8)+...+1/(2^n) = 2 - 1/(2^n) Thanks in advance
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Originally Posted by storchfire1X Hi I hope someone can help me with this problem: Prove the following formula by induction: 1+(1/2)+(1/4)+(1/8)+...+1/(2^n) = 2 - 1/(2^n) Thanks in advance A) Base case n=0, then the left hand side is 1, and the right hnd side is 1. B) Suppose this true for some Then: hence it is true for k+1. Thus combining A), and B) we have proven that it is true for all by mathematical induction RonL
Originally Posted by storchfire1X Hi I hope someone can help me with this problem: Prove the following formula by induction: 1+(1/2)+(1/4)+(1/8)+...+1/(2^n) = 2 - 1/(2^n) Thanks in advance n = 0 (Check!) Now assume this is true for some n = k. We wish to show that it is true for n = k + 1. So assume: is true. as we needed to show. -Dan
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