Question Number 148631 by tabata last updated on 29/Jul/21

find the region converge of the series and find the sum Σ_(n=1) ^∞ (n/(2^n (z−1)^n )) ?

Commented bytabata last updated on 29/Jul/21

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Answered by mathmax by abdo last updated on 30/Jul/21

u_n =(n/(2^n (z−1)^n )) ⇒∣(u_(n+1) /u_n )∣=∣((n+1)/(2^(n+1) (z−1)^(n+1) ))×((2^n (z−1)^n )/n)∣ =∣((n+1)/(2n(z−1)))∣→(1/(2∣z−1∣))<1 ⇒2∣z−1∣>1 ⇒∣z−1∣>(1/2) ⇒ donc la serie converge dans Λ={z ∈C /∣z−1∣>(1/2)}

Commented bySozan last updated on 30/Jul/21

sir and the sum how can find ?