Tính giới hạn \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaacM % gacaGGTbWaamWaaeaadaWcaaqaaiaaigdaaeaacaaIXaGaaiOlaiaa % iodaaaGaey4kaSYaaSaaaeaacaaIXaaabaGaaGOmaiaac6cacaaI0a % aaaiabgUcaRiaac6cacaGGUaGaaiOlaiaac6cacqGHRaWkdaWcaaqa % aiaaigdaaeaacaWGUbWaaeWaaeaacaWGUbGaey4kaSIaaGOmaaGaay % jkaiaawMcaaaaaaiaawUfacaGLDbaaaaa!4BE8! \lim \left[ {\frac{1}{{1.3}} + \frac{1}{{2.4}} + .... + \frac{1}{{n\left( {n + 2} \right)}}} \right]\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaacM % gacaGGTbWaamWaaeaadaWcaaqaaiaaigdaaeaacaaIXaGaaiOlaiaa % iodaaaGaey4kaSYaaSaaaeaacaaIXaaabaGaaGOmaiaac6cacaaI0a % aaaiabgUcaRiaac6cacaGGUaGaaiOlaiaac6cacqGHRaWkdaWcaaqa % aiaaigdaaeaacaWGUbWaaeWaaeaacaWGUbGaey4kaSIaaGOmaaGaay % jkaiaawMcaaaaaaiaawUfacaGLDbaacqGH9aqpciGGSbGaaiyAaiaa % c2gadaWcaaqaaiaaigdaaeaacaaIYaaaamaadmaabaWaaSaaaeaaca % aIYaaabaGaaGymaiaac6cacaaIZaaaaiabgUcaRmaalaaabaGaaGOm % aaqaaiaaikdacaGGUaGaaGinaaaacqGHRaWkcaGGUaGaaiOlaiaac6 % cacaGGUaGaey4kaSYaaSaaaeaacaaIYaaabaGaamOBamaabmaabaGa % amOBaiabgUcaRiaaikdaaiaawIcacaGLPaaaaaaacaGLBbGaayzxaa % aaaa!646C! \lim \left[ {\frac{1}{{1.3}} + \frac{1}{{2.4}} + .... + \frac{1}{{n\left( {n + 2} \right)}}} \right] = \lim \frac{1}{2}\left[ {\frac{2}{{1.3}} + \frac{2}{{2.4}} + .... + \frac{2}{{n\left( {n + 2} \right)}}} \right]\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaci % iBaiaacMgacaGGTbWaaSaaaeaacaaIXaaabaGaaGOmaaaadaqadaqa % aiaaigdacqGHsisldaWcaaqaaiaaigdaaeaacaaIZaaaaiabgUcaRm % aalaaabaGaaGymaaqaaiaaikdaaaGaeyOeI0YaaSaaaeaacaaIXaaa % baGaaGinaaaacqGHRaWkdaWcaaqaaiaaigdaaeaacaaIZaaaaiabgk % HiTmaalaaabaGaaGymaaqaaiaaiwdaaaGaaiOlaiaac6cacaGGUaGa % ey4kaSYaaSaaaeaacaaIXaaabaGaamOBaaaacqGHsisldaWcaaqaai % aaigdaaeaacaWGUbGaey4kaSIaaGOmaaaaaiaawIcacaGLPaaaaaa!52C9! = \lim \frac{1}{2}\left( {1 - \frac{1}{3} + \frac{1}{2} - \frac{1}{4} + \frac{1}{3} - \frac{1}{5}... + \frac{1}{n} - \frac{1}{{n + 2}}} \right)\) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaci % iBaiaacMgacaGGTbWaaSaaaeaacaaIXaaabaGaaGOmaaaadaqadaqa % aiaaigdacqGHRaWkdaWcaaqaaiaaigdaaeaacaaIYaaaaiabgkHiTm % aalaaabaGaaGymaaqaaiaad6gacqGHRaWkcaaIYaaaaaGaayjkaiaa % wMcaaiabg2da9maalaaabaGaaG4maaqaaiaaisdaaaGaaiOlaaaa!478A! = \lim \frac{1}{2}\left( {1 + \frac{1}{2} - \frac{1}{{n + 2}}} \right) = \frac{3}{4}.\)