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           10
find      ∑ (k+2)*3*2^k
         k=0

 Aug 7, 2016

Best Answer 

 #3
avatar+26396 
+10

           10
find      ∑ (k+2)*3*2^k
         k=0

 

10k=0(k+2)32k=310k=0(k+2)2k=3S10|We set  S10=10k=0(k+2)2k

 

S10=10k=0(k+2)2k=220+321+422++1129+122102S10=221+322++1029+11210+12211S102S10=220+21+22+23++29+2101221120+21+22+23++29+210=211121+22+23++29+210=2112S102S10=220+211212211(12)S10=220+211212211S10=21112211S10=211(121)S10=21111S10=11211

 

10k=0(k+2)32k=3S10=311211=33211=67584

 

laugh

 Aug 8, 2016
 #1
avatar
+5

sum_(k=0)^10 3 (k+2) 2^k = 67,584

 Aug 7, 2016
 #2
avatar+118696 
+5

           10
find      ∑ (k+2)*3*2^k
         k=0

 

10k=03(k+2)2k=310k=0(k+2)2k=3[(2)+(32)+(44)+(58)+(616)+(732)+(864)+(9128)+(10256)+(11512)+(121024)]

 

=67584 

 Aug 7, 2016
 #3
avatar+26396 
+10
Best Answer

           10
find      ∑ (k+2)*3*2^k
         k=0

 

10k=0(k+2)32k=310k=0(k+2)2k=3S10|We set  S10=10k=0(k+2)2k

 

S10=10k=0(k+2)2k=220+321+422++1129+122102S10=221+322++1029+11210+12211S102S10=220+21+22+23++29+2101221120+21+22+23++29+210=211121+22+23++29+210=2112S102S10=220+211212211(12)S10=220+211212211S10=21112211S10=211(121)S10=21111S10=11211

 

10k=0(k+2)32k=3S10=311211=33211=67584

 

laugh

heureka Aug 8, 2016

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