European Proceedings Logo

From Integrable Functions To Limits Of Sequences

Table 1:

f : 0,1 R Sequence n2·xn Sequence yn l i m n xn l i m n yn
1 k = 1 n 1 ln 1 + 1 n k = 1 n 1 + 1 n 1 e
x k = 1 n 1 ln 1 + 1 k k = 1 n 1 + k n 2 1 2 e
xp, pR + * k = 1 n 1 ln 1 + n p - 1 k p k = 1 n 1 + k p n p + 1 1 p + 1 e 1 p + 1
ln(1+x) k = 1 n 1 ln 1 + 1 n ln 1 + k n k = 1 n 1 + 1 n ln 1 + k n 2·ln2-1 4 e
x·ln(1+x) k = 1 n 1 ln 1 + 1 k ln 1 + k n k = 1 n 1 + k n 2 ln 1 + k n 1 4 e e 4
ln ( 1 + x ) 1 + x k = 1 n 1 ln 1 + n + k n 2 ln 1 + k n k = 1 n 1 + 1 n + k ln 1 + k n ln 2 2 2 2 ln 2
1 1 + x 2 k = 1 n 1 ln 1 + n 2 + k 2 n 2 k = 1 n 1 + 1 n 2 + k 2 ln( 2 +1) 2 +1
x 1 + x 2 k = 1 n 1 ln 1 + n 2 + k 2 n k k = 1 n 1 + k n 2 + k 2 2 -1 e 2 - 1
arctgx k = 1 n 1 ln 1 + 1 n a r c t g k n k = 1 n 1 + 1 n a r c t g k n π 4 - ln 2 2 4 e π 4 2
x·arctgx k = 1 n 1 ln 1 + 1 k a r c t g k n k = 1 n 1 + k n 2 a r c t g k n π 4 - 1 2 e π - 2 4
x·ex k = 1 n 1 ln 1 + 1 k e k n k = 1 n 1 + k n 2 e k n 1 e
1 + x 2 k = 1 n 1 ln 1 + 1 n 2 + k 2 k = 1 n 1 + n 2 + k 2 n 2 2 + ln ( 2 + 1 ) 2 e 2 ( 2 + 1 )
1 + x 2 k = 1 n 1 ln 1 + n k n 2 + k 2 k = 1 n 1 + k n 2 + k 2 n 3 2 2 - 1 3 e 2 - 1 3
1 - x 2 k = 1 n 1 ln 1 + 1 n 2 - k 2 k = 1 n 1 + n 2 - k 2 n 2 π 4 e π 4
1 - x 2 k = 1 n 1 ln 1 + n k n 2 - k 2 k = 1 n 1 + k n 2 - k 2 n 3 1 3 e 3
< Back to article