PART-I : MATHEMATICS Consider the following statements: 1. \lim_{n \\to\infty} {2^{n}+(-2)^{n}}/{2^{n}} does not exist II. \lim_{n \\to\infty} {3^{n}+(-3)^{n}}/{4^{n}} does not exist Then

Correct Answer is : I is true and II is false

KVPY 2020-21 SB SX Exam Previous Papers

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PART-I : MATHEMATICS

Consider the following statements:
1.

\lim ↙{n \→\∞} {2^{n}+(-2)^{n}}/{2^{n}}

does not exist
II.

\lim ↙{n \→\∞} {3^{n}+(-3)^{n}}/{4^{n}}

does not exist
Then

Solution:

\lim ↙{n \→\∞} {2^{n}+(-2)^{n}}/{2^{n}}

=\lim ↙{n \→\∞}1+(-1)^{n}={DNE}

\lim ↙{n \→\∞} {3^{n}+(-3)^{n}}/{4^{n}}

=\lim ↙{n \→\∞}({3}/{4})^{n}+({-3}/{4})^{n}=0+0=0

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