Question

can we use two different suppositions for a variable in two different terms of the same equation?
e.g.
2*c1+3*c2+{sumation 0-inf} k*(k+1)+ {sumation 2-inf}ck*(k-1) = 0

Answer 1

can we say:
let k=j+2 for 3rd term
and k=j for 4th term


[the equation is not real]

Answer 2

not sure what you are asking. Can you ask again in a different way, or post a specific problem you want to solve?

Answer 3

in a single eq we have number of terms having a variable k, can we make supposition for k for the specific term in the eq?

Answer 4

\[-c_{0}x + \sum_{k=0}^{\infty} c _{k} k(k+1)x^0 + \sum_{k=2}^{\infty} c_{k} k(k-1)x^1 = 0\]
is it legal to make a supposition like,
let k=j-2 for 3rd term and k=j for 4th term
which will turn the equation into
\[-c_{0}x + \sum_{j=2}^{\infty}c_{j-2}(j-2)(j-1)x^0 + \sum_{j=2}^{\infty}c_{j}j(j-1)x^1 = 0\]
?
?

Answer 5

is it legal to make a supposition like,
let k=j-2 for 3rd term and k=j for 4th term

I would call that "renaming" the variable. you can let k= j-2 (which also means j= k+2)
you will still get the same terms when you expand the summation, so it is ok to do this.

Answer 6

Q: renaming the variable k=j+2 for a term and k=j for the other one in the same eq? still legal?

Answer 7

yes. as long as you don't change the actual terms of the summation you can rename things.

in other words, summing k=0 to 2 of k is the same as summing j= -2 to 0 of (j+2)
in both cases, the summation is 0+1+2