Tính giới hạn \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaacM % gacaGGTbWaamWaaeaadaWcaaqaaiaaigdaaeaacaaIXaGaaiOlaiaa % ikdaaaGaey4kaSYaaSaaaeaacaaIXaaabaGaaGOmaiaac6cacaaIZa % aaaiabgUcaRiaac6cacaGGUaGaaiOlaiaac6cacqGHRaWkdaWcaaqa % aiaaigdaaeaacaWGUbWaaeWaaeaacaWGUbGaey4kaSIaaGymaaGaay % jkaiaawMcaaaaaaiaawUfacaGLDbaaaaa!4BE5! \lim \left[ {\frac{1}{{1.2}} + \frac{1}{{2.3}} + .... + \frac{1}{{n\left( {n + 1} \right)}}} \right]\)

Đặt  \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiabg2 % da9maalaaabaGaaGymaaqaaiaaigdacaGGUaGaaGOmaaaacqGHRaWk % daWcaaqaaiaaigdaaeaacaaIYaGaaiOlaiaaiodaaaGaey4kaSIaai % Olaiaac6cacaGGUaGaaiOlaiabgUcaRmaalaaabaGaaGymaaqaaiaa % d6gadaqadaqaaiaad6gacqGHRaWkcaaIXaaacaGLOaGaayzkaaaaaa % aa!48EF! A = \frac{1}{{1.2}} + \frac{1}{{2.3}} + .... + \frac{1}{{n\left( {n + 1} \right)}}\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG % ymaiabgkHiTmaalaaabaGaaGymaaqaaiaaikdaaaGaey4kaSYaaSaa % aeaacaaIXaaabaGaaGOmaaaacqGHsisldaWcaaqaaiaaigdaaeaaca % aIZaaaaiabgUcaRiaac6cacaGGUaGaaiOlaiabgUcaRmaalaaabaGa % aGymaaqaaiaad6gaaaGaeyOeI0YaaSaaaeaacaaIXaaabaGaamOBai % abgUcaRiaaigdaaaaaaa!48E7! = 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{n} - \frac{1}{{n + 1}}\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG % ymaiabgkHiTmaalaaabaGaaGymaaqaaiaad6gacqGHRaWkcaaIXaaa % aiabg2da9maalaaabaGaamOBaaqaaiaad6gacqGHRaWkcaaIXaaaaa % aa!4096! = 1 - \frac{1}{{n + 1}} = \frac{n}{{n + 1}}\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taci % iBaiaacMgacaGGTbWaamWaaeaadaWcaaqaaiaaigdaaeaacaaIXaGa % aiOlaiaaikdaaaGaey4kaSYaaSaaaeaacaaIXaaabaGaaGOmaiaac6 % cacaaIZaaaaiabgUcaRiaac6cacaGGUaGaaiOlaiaac6cacqGHRaWk % daWcaaqaaiaaigdaaeaacaWGUbWaaeWaaeaacaWGUbGaey4kaSIaaG % ymaaGaayjkaiaawMcaaaaaaiaawUfacaGLDbaacqGH9aqpciGGSbGa % aiyAaiaac2gadaWcaaqaaiaad6gaaeaacaWGUbGaey4kaSIaaGymaa % aacqGH9aqpciGGSbGaaiyAaiaac2gadaWcaaqaaiaaigdaaeaacaaI % XaGaey4kaSYaaSaaaeaacaaIXaaabaGaamOBaaaaaaGaeyypa0JaaG % ymaaaa!5F68! \Rightarrow \lim \left[ {\frac{1}{{1.2}} + \frac{1}{{2.3}} + .... + \frac{1}{{n\left( {n + 1} \right)}}} \right] = \lim \frac{n}{{n + 1}} = \lim \frac{1}{{1 + \frac{1}{n}}} = 1\)