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let-U-n-p-k-1-n-1-n-k-p-1-with-n-p-from-N-1-calculate-lim-n-U-n-p-for-p-2-2-prove-that-U-n-1-is-convergent-3-let-V-n-k-1-n-sin-1-n-k-2-find-lim-V




Question Number 29503 by abdo imad last updated on 09/Feb/18
let U_(n,p) = Σ_(k=1) ^n   (1/((n+k)^(p+1) )) with n,p from N^★   1) calculate lim_(n→+∞) U_(n,p)  for p≥2  2)prove that U_(n,1)  is convergent  3) let V_n = Σ_(k=1) ^n  sin((1/((n+k)^2 ))) find lim_∞  V_n  .
letUn,p=k=1n1(n+k)p+1withn,pfromN1)calculatelimn+Un,pforp22)provethatUn,1isconvergent3)letVn=k=1nsin(1(n+k)2)findlimVn.

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