What is the sum of \(1 \dfrac{1}{2}+ 4\dfrac{1}{6}+ 7 \dfrac{1}{12}+ 10 \dfrac{1}{20}...\) upto 20 terms?
12410/21
Integer parts 1, 4, 7, 10, … form an AP with \(a=1, d=3\). Sum of 20 terms:
\[S_I=\tfrac{20}{2}(2+19\cdot 3)=10\cdot 59=590\]
Fractional parts have denominators \(n(n+1)\), so the sum telescopes:
\[\sum_{n=1}^{20}\frac{1}{n(n+1)}=1-\frac{1}{21}=\frac{20}{21}\]
Total: \(590+\dfrac{20}{21}=\dfrac{12390+20}{21}=\dfrac{12410}{21}\).
Similar Questions
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
The value of \(9 \div [\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\div(\frac{3}{4}-\frac{1}{3})\;of\;\frac{2}{9}]\) is:
Simplify the following expression:
\(\rm \frac{7}{12} \div \frac{1}{10} \ of \ \frac{2}{3} - \frac{5}{3} \times \frac{9}{10} + \frac{5}{8} \div \frac{3}{4} \ of \ \frac{2}{3}\)
value of \(3\frac{5}{6}+\left[3\frac{2}{3}+\lbrace{\frac{15}{4}\left(5\frac{4}{5}\div 14\frac{1}{2}\right)\rbrace}\right]\) is equal to:
Three fractions x, y and z are such that x > y > z. When the smallest of them is divided by the greatest, the result is \({\frac{9}{16}}\) , which exceeds y by 0.0625. If x + y + z = \(2{\frac{3}{12}}\) , then what is the value of x + z?
- The value of \(\frac{46+\frac{3}{4} \ \text{of}\ 32-6}{37-\frac{3}{4} \ \text{of}\ (34+6)}\) is:
simplify the following expression:
\(\rm\left(\frac{3}{4}-\frac{1}{4}\div\frac{1}{4}\ of\ \frac{2}{5}\right)\div\left(\frac{3}{4}\div\frac{2}{3}\ of\ \frac{3}{5}\right)\)
The value of \(\frac{52-1170\div26+13\times2}{2+1\frac{1}{8}\ \rm of\ 2-1\frac{1}{4}}\) is:
The value of 25 ÷ 15 of 4 × [4 ÷ 5 × (9 - 7)] - (20 ÷ 5 of 9) is:
Important Questions from Fractions
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
Among the fractions \(\frac{7}{12}\) , \(\frac{8}{15}\) , \(\frac{17}{24}\) and \(\frac{13}{18}\) , which is the smallest?
