How would I prove that for any a > 1, 1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a)
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Originally Posted by thamathkid1729 How would I prove that for any a > 1, 1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a) Observer that for $\displaystyle a>1$: $\displaystyle \dfrac{1}{a+1}\ge \dfrac{1}{a+n}$ where $\displaystyle $$ n$ is a positive integer
Originally Posted by thamathkid1729 How would I prove that for any a > 1, 1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a) $\displaystyle \displaystyle{\frac{1}{a+1}+\frac{1}{a+2}+\ldots +\frac{1}{a^2}\geq \frac{a^2-a}{a^2}}$ Tonio
E=1/(a+1)+1/(a+2)...1/a^2 E>N/(a+1) N=a^2-a E>(a^2-a)/(a+1)>(a^2-a)/a^2 I want a real challenge
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