If a_n >0 and lim_(n→∞) a_n = 0 Find: lim_(n→∞) (1/n) Σ_(k=1) ^n ln ((k/n) + a_n ) = ?
∫(dx/(x^(15) −x^(11) ))
(y^(′′) /y) = 4x^2 + 2
If Σ a_n is absolutely convergent, prove that Σ (a_n /n) is also absolutely convergent.
{ ((x + y + z = 1)),((42x + 44y + 30z = 42)) :} (x,y,z)=(1,0,0) yes, but solution...
Evaluate : B_n = Π_(k=3) ^n (( k^( 2) −1)/(k^2 + k −6))= ?
m , n ∈ N m ≥ 2 and n ≥ 2 p > 0 and q > 0 p + q = 1 Prove that: (1−q^n )^m + (1−p^m )^n ≥ 1
a^2 −a−^(1000) (√((1+8000a)))=1000 find a
6 different letters were written to 6 different people and 6 different envelopes were prepared with the addresses of these people written on them. In how many different ways can you put a letter in each envelope without putting a letter written to this person in the envelope with the name of any person?
If x + ((49)/(x + 48)) = − 34 find (2x + 83)^3 + (1/((2x + 83)^3 ))
Arrange in descending order: (√5) − (√2), (√7) − (√5) , (√(13)) − (√(11)) , (√(19)) − (√(17))
:: α , β and γ are roots of the following equation . Find the value of ” F ” : Equation : x^( 3) −2x −1=0 F := α^( 5) + β^( 5) + γ^( 5)
prove : curve { ((x(t)=((a+r.cos(t))/(a^2 +r^2 +2ar.cos(t))))),((y(t)=((r.sin(t))/(a^2 +r^2 +2ar.cos(t))))) :} 0≤t≤2π is circle , find center & radius
The cost of maintaining a school is partly constant and partly varies as the number of students. With 50 students the cost is $15705 and with 40 students the cost is$13305. If the fee per student is \$360.00, what is the least number of students for which the school can be run without loss?
Compare: 8! and 8!!