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Question Number 106001 by Algoritm last updated on 02/Aug/20

Answered by JDamian last updated on 02/Aug/20

5056(e−1)

$$\mathrm{5056}\left({e}−\mathrm{1}\right) \\ $$

Answered by mr W last updated on 02/Aug/20

=Σ_(n=0) ^(5055) ∫_n ^(n+1) e^({x}) dx  =Σ_(n=0) ^(5055) ∫_0 ^1 e^t dt  =5056(e−1)

$$=\underset{{n}=\mathrm{0}} {\overset{\mathrm{5055}} {\sum}}\int_{{n}} ^{{n}+\mathrm{1}} {e}^{\left\{{x}\right\}} {dx} \\ $$$$=\underset{{n}=\mathrm{0}} {\overset{\mathrm{5055}} {\sum}}\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{t}} {dt} \\ $$$$=\mathrm{5056}\left({e}−\mathrm{1}\right) \\ $$

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