Wednesday, 11 June 2014

summation - Calculating sums




My maths teacher showed me something on how to calculate sums. Let's take an example:



nk=1k(k+1)=nk=1k2+nk=1k=n(n+1)(2n+1)6+n(n+1)2=n(n+1)(n+2)3



This was an easy one, but I just can't understan how to solve such sums:



nk=1(k1)k(k+1)




nk=11(3n2)(3n+1)



Could anybody help me, please?



I want to understand the idea of solving sums like these, so please, do not be very specific, but help me giving these and maybe some other examples.


Answer



HINT:



The second example is orthogonal to the first, hence a different answer




3(3n+1)(3n2)=(3n+1)(3n2)(3n+1)(3n2)=13n213n+1



Set a few values of n=1,2,3,,n2,n1,n to recognize the Telescoping Series


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