Tính giới hạn \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaacM % gacaGGTbWaamWaaeaadaqadaqaaiaaigdacqGHsisldaWcaaqaaiaa % igdaaeaacaaIYaWaaWbaaSqabeaacaaIYaaaaaaaaOGaayjkaiaawM % caamaabmaabaGaaGymaiabgkHiTmaalaaabaGaaGymaaqaaiaaioda % daahaaWcbeqaaiaaikdaaaaaaaGccaGLOaGaayzkaaGaaiOlaiaac6 % cacaGGUaWaaeWaaeaacaaIXaGaeyOeI0YaaSaaaeaacaaIXaaabaGa % amOBamaaCaaaleqabaGaaGOmaaaaaaaakiaawIcacaGLPaaaaiaawU % facaGLDbaaaaa!4E04! \lim \left[ {\left( {1 - \frac{1}{{{2^2}}}} \right)\left( {1 - \frac{1}{{{3^2}}}} \right)...\left( {1 - \frac{1}{{{n^2}}}} \right)} \right]\)

Cách 1: 

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaacM % gacaGGTbWaamWaaeaadaqadaqaaiaaigdacqGHsisldaWcaaqaaiaa % igdaaeaacaaIYaWaaWbaaSqabeaacaaIYaaaaaaaaOGaayjkaiaawM % caamaabmaabaGaaGymaiabgkHiTmaalaaabaGaaGymaaqaaiaaioda % daahaaWcbeqaaiaaikdaaaaaaaGccaGLOaGaayzkaaGaaiOlaiaac6 % cacaGGUaWaaeWaaeaacaaIXaGaeyOeI0YaaSaaaeaacaaIXaaabaGa % amOBamaaCaaaleqabaGaaGOmaaaaaaaakiaawIcacaGLPaaaaiaawU % facaGLDbaacqGH9aqpciGGSbGaaiyAaiaac2gadaWadaqaamaabmaa % baGaaGymaiabgkHiTmaalaaabaGaaGymaaqaaiaaikdaaaaacaGLOa % GaayzkaaWaaeWaaeaacaaIXaGaey4kaSYaaSaaaeaacaaIXaaabaGa % aGOmaaaaaiaawIcacaGLPaaadaqadaqaaiaaigdacqGHsisldaWcaa % qaaiaaigdaaeaacaaIZaaaaaGaayjkaiaawMcaamaabmaabaGaaGym % aiabgUcaRmaalaaabaGaaGymaaqaaiaaiodaaaaacaGLOaGaayzkaa % GaaiOlaiaac6cacaGGUaWaaeWaaeaacaaIXaGaeyOeI0YaaSaaaeaa % caaIXaaabaGaamOBaaaaaiaawIcacaGLPaaadaqadaqaaiaaigdacq % GHRaWkdaWcaaqaaiaaigdaaeaacaWGUbaaaaGaayjkaiaawMcaaaGa % ay5waiaaw2faaaaa!7281! \lim \left[ {\left( {1 - \frac{1}{{{2^2}}}} \right)\left( {1 - \frac{1}{{{3^2}}}} \right)...\left( {1 - \frac{1}{{{n^2}}}} \right)} \right] = \lim \left[ {\left( {1 - \frac{1}{2}} \right)\left( {1 + \frac{1}{2}} \right)\left( {1 - \frac{1}{3}} \right)\left( {1 + \frac{1}{3}} \right)...\left( {1 - \frac{1}{n}} \right)\left( {1 + \frac{1}{n}} \right)} \right]\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % yEamaaCaaaleqabaGaamOBaaaakiabgkHiTiaadIhadaahaaWcbeqa % aiaad6gaaaGccqGH9aqpcaGGOaGaamyEaiabgkHiTiaadIhacaGGPa % GaaiikaiaadMhadaahaaWcbeqaaiaad6gacqGHsislcaaIXaaaaOGa % ey4kaSIaamyEamaaCaaaleqabaGaamOBaiabgkHiTiaaigdaaaGcca % WG4bGaey4kaSIaaiOlaiaac6cacaGGUaGaey4kaSIaamiEamaaCaaa % leqabaGaamOBaiabgkHiTiaaigdaaaGccaGGPaaaaa!5554! \Rightarrow {y^n} - {x^n} = (y - x)({y^{n - 1}} + {y^{n - 1}}x + ... + {x^{n - 1}})\) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % yEaiabgkHiTiaadIhacqGH9aqpdaWcaaqaaiaadMhadaahaaWcbeqa % aiaad6gaaaGccqGHsislcaWG4bWaaWbaaSqabeaacaWGUbaaaaGcba % GaamyEamaaCaaaleqabaGaamOBaiabgkHiTiaaigdaaaGccqGHRaWk % caWG5bWaaWbaaSqabeaacaWGUbGaeyOeI0IaaGymaaaakiaadIhacq % GHRaWkcaGGUaGaaiOlaiaac6cacqGHRaWkcaWG4bWaaWbaaSqabeaa % caWGUbGaeyOeI0IaaGymaaaaaaaaaa!52A8! \Rightarrow y - x = \frac{{{y^n} - {x^n}}}{{{y^{n - 1}} + {y^{n - 1}}x + ... + {x^{n - 1}}}}\)

Cách 2: Bấm máy tính như sau: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H49aaC % beaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcqGHRaWk % cqGHEisPaeqaaOGaaiikaiaadMhacqGHsislcaWG4bGaaiykaiabg2 % da9maaxababaGaciiBaiaacMgacaGGTbaaleaacaWG4bGaeyOKH4Qa % ey4kaSIaeyOhIukabeaakmaalaaabaGaamyEamaaCaaaleqabaGaam % OBaaaakiabgkHiTiaadIhadaahaaWcbeqaaiaad6gaaaaakeaacaWG % 5bWaaWbaaSqabeaacaWGUbGaeyOeI0IaaGymaaaakiabgUcaRiaadM % hadaahaaWcbeqaaiaad6gacqGHsislcaaIYaaaaOGaamiEaiabgUca % Riaac6cacaGGUaGaaiOlaiabgUcaRiaadIhadaahaaWcbeqaaiaad6 % gacqGHsislcaaIXaaaaaaaaaa!64A2! \Rightarrow \mathop {\lim }\limits_{x \to + \infty } (y - x) = \mathop {\lim }\limits_{x \to + \infty } \frac{{{y^n} - {x^n}}}{{{y^{n - 1}} + {y^{n - 2}}x + ... + {x^{n - 1}}}}\) và so đáp án (có thể thay 100 bằng số nhỏ hơn hoặc lớn hơn).