Sum Rule - Page 3

Questions
  • What is the sum of this geometric series. #sum2(3)^( n-1)# for n=1 to 6?
  • If #y=e^(msin^-1x)#, then show that #(1-x^2)y_2-xy_1=m^2y#?
  • How do you evaluate #\sum _ { k = 0} ^ { n } ( 3- 2k )#?
  • What is the sum of the multiples of #7# between #91# and #707# inclusive?
  • How do I convert #lim_(n->oo) sum_(i=0)^n (12n)/(16n^2 + 9i^2)# into a definite integral?
  • Area under the curve of x^3 from -1 to 3 with Summation?
  • #lim_(n->oo)sum_(k=0)^n((pi/2 k/n)^2+(pi/2 k/n)cos(pi/2 k/n)) (pi/2 1/n)=# ?
  • #lim_(x->2)( x - 2) / ( sqrt ( x - 1) + 2 root(4) ( x - 1) -3) =# ?
  • If #y=ln[x+sqrt(x^2+1)]#, check whether #(1+x^2)y_(n+2) + (2n+1)xy_(n+1) - n^2y_n=0# is true or not?
  • How do I differentiate #50sum_(i=1)^x(1.03^i)#?
  • Let f(x) = -2 x + 5 x^2. Then the expression (f(x+h)-f(x))/h?
  • Can you help me find the indicated sum? Thanks!
  • How do I find f'(x) of f(t)=9/(t^3)?
  • How do I solve f'(x) for f(x)=7(x^2)+(2/(x^2))?
  • How do I find f'(x) for f(x)=7(x^(4/5))-8(x^(6/7))?
  • How to calculate sum of this? #sum_(n=1)^oo(-1)^n n(n-1)x^n#
  • How you calculate this?#sum_(n=1)^oo arctan((n+1)/(n^3+1))#
  • Approximate #sum_(n=1)^oo(-1)^n/((3^n)(n!))# correct to four decimal places?
  • How can i solve this?
  • What is equal ? #lim_(x->pi/2)sin(cosx)/(cos^2(x/2) -sin^2(x/2) )= ?#