Question Number 84783 by Power last updated on 16/Mar/20
Commented by Power last updated on 16/Mar/20
$$\mathrm{k}=\mathrm{3} \\ $$
Commented by Tony Lin last updated on 16/Mar/20
$${what}\:{does}\:{k}=\mathrm{3}\:{mean}? \\ $$
Commented by Power last updated on 16/Mar/20
$$\mathrm{k}\neq\mathrm{1}\:\:\Rightarrow\:\mathrm{k}=\mathrm{3}\:\:\:\:\mathrm{instaed}\:\mathrm{of}\:\mathrm{k}=\mathrm{1} \\ $$
Commented by Power last updated on 16/Mar/20
$$\mathrm{please}\:\mathrm{see} \\ $$
Commented by Power last updated on 16/Mar/20
$$\mathrm{sir}\:\mathrm{MJS}\:\mathrm{pls} \\ $$
Commented by Tony Lin last updated on 16/Mar/20
$${i}\:{don}'{t}\:{know}\:{the}\:{quick}\:{way}\:{to}\:{evaluate} \\ $$$${the}\:{answer} \\ $$$${but}\:{the}\:{answer}\:{is}\:{very}\:{ugly} \\ $$$$\frac{\mathrm{364219040265251}}{\mathrm{13127595717600}} \\ $$$$\fallingdotseq\mathrm{27}.\mathrm{7445351} \\ $$$${it}\:{seems}\:{that}\:{there}\:{is}\:{no}\:{quick}\:{way}\: \\ $$$${to}\:{solve} \\ $$$${just}\:{add}\:{altogether} \\ $$
Answered by mind is power last updated on 16/Mar/20
$$=\underset{{k}=\mathrm{1}} {\overset{\mathrm{32}} {\sum}}\left(\mathrm{1}−\frac{\mathrm{1}}{{k}+\mathrm{1}}\right) \\ $$$$=\mathrm{32}−\underset{{k}=\mathrm{1}} {\overset{\mathrm{32}} {\sum}}\frac{\mathrm{1}}{{k}+\mathrm{1}}=\mathrm{32}−\underset{{k}=\mathrm{2}} {\overset{\mathrm{33}} {\sum}}\frac{\mathrm{1}}{{k}}=\mathrm{33}−{H}_{\mathrm{33}} \\ $$
Commented by Power last updated on 16/Mar/20
$$\mathrm{thanks}\:\:\:\mathrm{H}_{\mathrm{33}} \:\:−? \\ $$
Commented by mind is power last updated on 16/Mar/20
$${H}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}} \\ $$