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Problem Which of the following limits is equal to ∫ 1 4 2 x d x \displaystyle\int_{1}^{4} 2x\,dx ∫ 1 4 2 x d x lim n → ∞ ∑ i = 1 n ( 1 + 3 i n ) 3 n \displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}\left(1+\frac{3i}{n}\right)\frac{3}{n} n → ∞ lim i = 1 ∑ n ( 1 + n 3 i ) n 3 lim n → ∞ ∑ i = 1 n 2 ( 1 + 3 i n ) 3 n \displaystyle \lim_{n\to\infty}\sum_{i=1}^{n} 2\!\left(1+\frac{3i}{n}\right)\frac{3}{n} n → ∞ lim i = 1 ∑ n 2 ( 1 + n 3 i ) n 3 lim n → ∞ ∑ i = 1 n 2 ( 1 + 3 i n ) 1 n \displaystyle \lim_{n\to\infty}\sum_{i=1}^{n} 2\!\left(1+\frac{3i}{n}\right)\frac{1}{n} n → ∞ lim i = 1 ∑ n 2 ( 1 + n 3 i ) n 1 lim n → ∞ ∑ i = 1 n 2 ( 1 + i n ) 3 n \displaystyle \lim_{n\to\infty}\sum_{i=1}^{n} 2\!\left(1+\frac{i}{n}\right)\frac{3}{n} n → ∞ lim i = 1 ∑ n 2 ( 1 + n i ) n 3 Browse the problem library