Statement: Let (an) be a sequence of positive terms lim n->infinity a power 1/n = lim n->infinity an+1/an. Provided the limit on t...
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Important Basic Theorem
Statement: Let (an) be any sequence. And lim n -> infinity (an/an+1) = l if l > 1 then, (an) -> 0. Proof: Let, k be any re...
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Application Of Mathematics
Just you are see in Mathematics in our Natural Life, I will explain in Natural and Daily Life use in Mathematics, Just see the PDF File...
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SEQUENCE - CESARO'S THEOREM
Statement: Cesaro's theorem if (an) ->a, and (bn) ->b then (a1bn+a2bn-2+anb1/n) ->ab. proof: Let, cn = a1bn+........
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WORLD BEST MATHEMATICIAN TERENCE TAO IN AUSTRALIA
Tao at March 2006 Erdos Memorial Conference in Memphis, Tennessee. Born 17 July 1975 (age 41) Adelaide, South Austra...
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Sum Theorem's on Limits - Cauchy's First Limit Theorem
Statement: If (an) -> l, then (a1+a2+....+an/n) -> l. Proof: Case(i): Let l = 0. Let, bn = a1+a2+......+an/n. Let excellon...
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Virat Indian Test Team Revenge in Aus Exculsive Remix
BY DETICATED IN INDIAN FANS & PEOPLES
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Show that if (an) ->0 and (bn) is bounded, then (anbn) ->0
Since (bn) is bounded, there exist k >0 such that mod bn <=k for all n. Therefore, mod anbn <= k mod an Now, let excellon >0...
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Discuss the Behaviour of the Geometric Sequence (r power n)
Proof: Case (i): Let, r =0. Then, (r power n) Reduces to the constant sequence. 0,0,0,.... and hence convergences to 0. Case (ii...
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A SEQUENCE CANNOT CONVERGE TO TWO DIFFERENT LIMITS
I am proof this statement, please following: Let (an) be a Convergent Sequence. If possible let l1 and l2 be two different limits of (a...
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CONVERGENCE SEQUENCE
Definition: A sequence (an) is convergence to a number l. If given excellon >0 there exist a positive integer m. Such that mod an -...
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MONOTONIC SEQUENCE
Definition: A sequence (an) is set to be (i) monotonic increasing if an<=an+1 (ii) Strictly monotonic increasing if an<an+1 (iii...
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BOUNDED SEQUENCE
Definition: A sequence (an) set to be bounded above if there exists a real number k such that an<=k for all n belongs to N then k is...
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SEQUENCE AND SERIES
Definition: Let f:N->R be a function and let f(n)=an. Then, a1,a2,a3,...,an,.... is called the sequences in R deter mind by the ...
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LOSS OF KINETIC ENERGY DUE TO OBLIQUE IMPACT OF TWO SMOOTH SPHERES
Two spheres of masses m1 and m2, moving with velocities u1 and u2 angles (alpha)𝝰1 and 𝝰2 with their line of centres, come into col...
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Dynamics - Loss of kinetic energy due to direct impact of two smooth spheres
Two spheres of given masses with given velocities impinge directly; to show that there is a loss of kinetic energy and to find the...
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Dynamics- Dissipation of energy due to impact
We have found that in any impact, except where the coefficient of restitution is unity, some kinetic energy is lost. This missing kinet...
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Notification 1
Sorry friends. Delay for the content today. Then delay problems not comes in Future. And many useful mathematical contents i am post her...
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DYNAMICS-COLLISION OF ELASTIC BODIES
Direct impact of two smooth spheres: A smooth sphere of mass m1 impinges directly with velocity u1 on another smooth sphere of ma...
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Dynamics-Oblique Impact of Two Smooth Spheres
A smooth sphere of mass m1 impinges obliquely with velocity u1 an another smooth sphere of mass m2 moving with velocity u2. If the...
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Force necessary to produce Simple Harmonic Motion
Definition: If F is the force required to produce an acceleration f in a particle of mass m, then by Newton's Second Law of motion....
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SACHIN A BILLON DREAMS Coming Soon..
From a Wild Child To a Virtuous Hero ONE MAN UNITED HIS COUNTRY From EMMY NOMINATED DIRECTOR JAMES ERSKINE MUSIC BY ACADEMY AWARD WINN...
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SIMPLE HARMONIC MOTION IN A Straight Line
Definition: When a particle moves in a straight line so that its acceleration is always directed towards a fixed point in the line...
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SIMPLE HARMONIC MOTION
INTRO A very common and important type of motion occurring in nature is that which involves oscillations backwards and forwards about so...
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MATHS Authors AND Explains
Today I will started for Mathematical Posts to Continously. Thanks Guyz...
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