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Question Number 88462 by M±th+et£s last updated on 10/Apr/20

Commented by mathmax by abdo last updated on 10/Apr/20

$$S_n={\int }_{7n+1}^{22n}\frac{dt}{2t+1}\Rightarrow S_n={\left[\frac{1}{2}ln(2t+1)\right]}_{7n+1}^{22n}$$$$=\frac{1}{2}(ln(44n+1)-ln(14n+1))$$$$=\frac{1}{2}ln\left(\frac{44n+1}{14n+1}\right)\Rightarrow {lim}_{n\to +\mathrm{\infty }}{S}_n=\frac{1}{2}ln\left(\frac{44}{14}\right)=\frac{1}{2}ln\left(\frac{22}{7}\right)$$

Commented by M±th+et£s last updated on 10/Apr/20

$$thankyousir$$

Commented by turbo msup by abdo last updated on 11/Apr/20

$$youarewelcome$$

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