If limn→∞ ∑$$k=0n$$ $$nCknk(k+3)=e$$−λ then λ$$=$$

Question

If limn→∞ ∑$$k=0n$$  $$nCknk(k+3)=e$$−λ then λ$$=$$

Infinity Learn · Accepted Answer

limn→∞ $$k=0n$$ $$nCknkk+3=limn$$→∞ $$k=0n1k+3$$⋅nCk⋅$$1nk$$                                 $$=limn$$→∞ $$k=0nCk$$   n⋅$$1nk$$∫$$01xk+2dx$$                                 $$=$$∫$$01x2limn$$→∞ $$k=0nxnkdx$$                                 $$=$$∫$$01x2$$⋅limn→∞$$1+xnndx$$                                 $$=$$∫$$01x2exdx$$                                $$=e$$−$$2$$

$If lim_{n \to \infty} \sum_{k = 0}^{n} \frac{^{n} C_{k}}{n^{k} (k + 3)} = e - λ then λ =$

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If limn→∞ ∑k=0n nCknk(k+3)=e−λ then λ=

Remember concepts with our Masterclasses.

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$If lim_{n \to \infty} \sum_{k = 0}^{n} \frac{^{n} C_{k}}{n^{k} (k + 3)} = e - λ then λ =$