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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.3 Summation versus Integration, #31 · Calculus · Integrals

Find the flaw in the proof that … for every

Find the flaw in the proof that $2^{n} = 1$ for every $n = 0, 1, 2, \dots$ . For $n = 0$ we have $2^{0} = 1$ . If $2^{n} = 1$ for every $n < N$ , then $2^{N} = 2^{N - 1} \cdot 2^{N - 1} / 2^{N - 2} = 1 \cdot 1/1 = 1$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.3 Summation versus Integration, #31

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