Exponential and logarithmic series: Find the sum of

Guadalupe Glass

Guadalupe Glass

Answered question

2022-04-02

Exponential and logarithmic series: Find the sum of
22+322!+423!+ to infinity

Answer & Explanation

arrebusnaavbz

arrebusnaavbz

Beginner2022-04-03Added 18 answers

So,
Tn=(n+1)2n!
Let (n+1)2=n(n1)+Bn+C
n2+2n+1=n2+n(B1)+C
B1=2,B=3,C=1
So,
Tn=(n+1)2n!=1(n2)!+31(n1)!+1n!
Putting n=0,1,2,3,
T0=10!
T1=0+310!+11!
T2=10!+311!+12!
T3=11!+312!+13!

So,  0r<(n+1)2n!=e+3e+e
So,  1r<(n+1)2n!=e+3e+e(0+1)20!=5e1

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