AP EAMCET · Maths · Definite Integration
\(\lim _{x \rightarrow \infty} \frac{1^{77}+2^{77}+\ldots+n^{77}}{n^{78}}=\)
- A \(\frac{1}{77}\)
- B 1
- C 76
- D \(\frac{1}{78}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{78}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \lim _{n \rightarrow \infty} \frac{1^{77}+2^{77}+\ldots+n^{77}}{n^{78}} \\ & =\lim _{n \rightarrow \infty} \frac{1}{n}\left(\frac{1^{77}}{n^{77}}+\frac{2^{77}}{n^{77}}+\ldots+\frac{n^{77}}{n^{77}}\right) \\ & =\lim _{n \rightarrow \infty} \frac{1}{n}…
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