Which of the series converge and
which diverge? Check by the limit
comparison test.
1) Σ_(n=2) ^∞ ((1+n ln(n))/(n^2 +5))
2) Σ_(n=1) ^∞ ((ln(n))/n^(3/2) )
3) Σ_(n=3) ^∞ (1/(ln(lnn)))
4) Σ_(n=1) ^∞ (1/(n (n)^(1/n) ))
??
Find the third degree polynomial which vanishes when
x =−1 and x = 2, which has a value 8 when x =0 and leaves a remainder ((16)/3) when
divided by 3x + 2.
solve for real x and y:[a,b∈R]
a. { ((x^3 +1=y^3 )),((x^2 +1=y^2 )) :}
b. { ((x^3 +x^2 +1=y^3 )),((x^2 +x+1=y^2 )) :}
c. { ((x^3 +y^2 =9xy)),((x^2 +y^3 =8xy)) :}
d. { ((ax+by=2ab)),((x^2 +y^2 =4abxy)) :}