\lim_{n\to\infty} \frac{(1+n)^7+(2+n)^7+.....+(7+n)^7}{1000+n^7}

TS ICET 23 May 2018 Shift 2 Paper

Question : 135 of 200

Marks: +1, -0

\lim↙{n→∞} {(1+n)^7+(2+n)^7+.....+(7+n)^7}/{1000+n^7}

Solution:

When

n→ ∞ \;{1}/{ n } → 0

\lim ↙{n → ∞} \;{(1+n)^{7}+(2+n)^{7}+⋅s(7+n)^{7}}/{1000+n^{7}}

\lim ↙{n → ∞} \;{n^{7}\{(1+{1}/{n})^{7}+(1+{2}/{n})^{7}+⋅s+(1+{7}/{n})^{7}\}}/{n^{7}(1+\;{1000}/{n^{7}})}

=\;{1+1+1+1+1+1+1}/{1}=7

Go to Question:

Prev Question

Next Question