I have a series in which the general term is represented by
an=kn+1−k−nk+n(k−1)2
where k is a constant.
How do I derive the formula for ∑n=bn=1Sn (summation of n terms)?
I'm not really good at mathematics (high school level), so kindly explain it in the simplest way possible.
Answer
HINT
Note that you can divide and sum each part separately
an=kn+1−k−nk+n(k−1)2=kn+1−k(k−1)2−nk−n(k−1)2=kn+1(k−1)2−k(k−1)2−n(k−1)
and
n=b∑n=1kn+1=n=b−1∑n=0kn+2=k2n=b−1∑n=0kn=k21−kb1−k
n=b∑n=1n=b(b+1)2
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