4+44+444+ … … ধারাটির n তম পদের যোগফল কত?

A 4/9{10/9(10n - 1) -n}

B 4/9{9/10(10n - 1) -n}

C 9/4{9/10(10n - 1) -n}

D 9/4{10/9(10n - 1) -n}

Solution

Correct Answer: Option A

S = 4+44+444+......n-পদ পর্যন্ত
9S/4 = 9+99+999+...n-পদ পর্যন্ত
=(10-1)+(100-1)+(1000-1)+....n-পদ পর্যন্ত
=(101-1)+(102-1)+(103-1)+....n-পদ পর্যন্ত
=101+102+103+...+10n -n
=10(1+10+102+..+10n-1) -n
=10{(10n-1)/(10-1)} -n
=10/9(10n- 1) -n
∴S = 4/9{10/9(10n - 1) -n}

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