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Among (S1): lim n→∞ 1/n^2 (2 + 4 + 6 + ...... + 2n) = 1 (S2): lim n→∞ 1/16 (1^15 + 2^15 + 3^15 + ...... + n^15) = 1/16 (1) Both (S1) and (S2) are true (2) Only (S1) is true (3) Both (S1) and (S2) are false (4) Only (S2) is true

1. Both (S1) and (S2) are true
2. Only (S1) is true
3. Both (S1) and (S2) are false
4. Only (S2) is true

Correct answer: Both (S1) and (S2) are true

Solution

Both statements are true as they correctly evaluate the limits using appropriate mathematical principles. In S1, the sum of the first n even numbers simplifies to n(n+1), and dividing by n^2 leads to a limit of 1. In S2, the sum of the first n integers raised to the 15th power divided by 16 approaches 1/16 as n approaches infinity.

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