Find the value of the following without addition:$1+3+5+7+9+11+13+15+17+19+21$
Given:
The given expression is $1+3+5+7+9+11+13+15+17+19+21$.
To do :
We have to find the sum of the given expression without adding.
Solution :
We know that,
The sum of 'n' consecutive odd numbers is $n^2$.
In the given sum there are 11 consecutive odd numbers.
Therefore,
$n =11$
$n^2 = 11^2 =121$.
Therefore, the value of $1+3+5+7+9+11+13+15+17+19+21$ is $121$.
Related Articles
- Without adding, find the sum.(i) \( 1+3+5+7+9 \)(ii) \( 1+3+5+7+9+11+13+15+17+19 \)(iii) \( 1+3+5+7+9+11+13+15+17+19+21+23 \)
- Without adding, find the sum of the following:$1+3+5+7+9+11+13$
- Solve the following:$3(5 z-7)-2(9 z-11)=4(8 z-13)-17$.
- Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:(i) \( \frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3} \)(ii) \( \frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9} \)(iii) \( \frac{2}{5}+\frac{8}{3}+\frac{-11}{15}+\frac{4}{5}+\frac{-2}{3} \)(iv) \( \frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{21} \)
- Find:$(i)$. $\frac{7}{24\ }- \frac{17}{36}$$(ii)$. $\frac{5}{63}-\ (-\frac{6}{21})$$(iii)$. $-\frac{6}{13}\ -\ (-\frac{7}{15})$$(iv)$. $-\frac{3}{8}-\frac{7}{11}$$(v)$. $-2\frac{1}{9}\ -\ 6$
- Re-arrange suitably and find the sum in each of the following:(i) \( \frac{11}{12}+\frac{-17}{3}+\frac{11}{2}+\frac{-25}{2} \)(ii) \( \frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7} \)(iii) \( \frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3} \)(iv) \( \frac{4}{13}+\frac{-5}{8}+\frac{-8}{13}+\frac{9}{13} \)(v) \( \frac{2}{3}+\frac{-4}{5}+\frac{1}{3}+\frac{2}{5} \)(vi) \( \frac{1}{8}+\frac{5}{12}+\frac{2}{7}+\frac{7}{12}+\frac{9}{7}+\frac{-5}{16} \)
- Without actually calculating the cubes, find the value of each of the following:(i) \( (-12)^{3}+(7)^{3}+(5)^{3} \)(ii) \( (28)^{3}+(-15)^{3}+(-13)^{3} \)
- Simplify and solve the following linear equations.\( 3(5 z-7)-2(9 z-11)=4(8 z-13)-17 \).
- Multiply:(i) \( \frac{7}{11} \) by \( \frac{5}{4} \)(ii) \( \frac{5}{7} \) by \( \frac{-3}{4} \)(iii) \( \frac{-2}{9} \) by \( \frac{5}{11} \)(iv) \( \frac{-3}{17} \) by \( \frac{-5}{-4} \)(v) \( \frac{9}{-7} \) by \( \frac{36}{-11} \)(vi) \( \frac{-11}{13} \) by \( \frac{-21}{7} \)(vii)\( -\frac{3}{5} \) by \( -\frac{4}{7} \)(viii) \( -\frac{15}{11} \) by 7
- If the polynomial $x^{19}+x^{17}+x^{13}+x^{11}+x^{7}+x^{5}+x^{3}$ is divided by $( x^{2}-1)$, then find the remainder.
- Which of the following are like fractions $\frac{6}{17}, \frac{18}{7}, \frac{17}{9}, \frac{7}{17}, \frac{21}{19}, \frac{32}{17}, \frac{12}{17}$.
- Express each of the following as a rational number of the form $\frac{p}{q}$(i) \( -\frac{8}{3}+\frac{-1}{4}+\frac{-11}{6}+\frac{3}{8}-3 \)(ii) \( \frac{6}{7}+1+\frac{-7}{9}+\frac{19}{21}+\frac{-12}{7} \)(iii) \( \frac{15}{2}+\frac{9}{8}+\frac{-11}{3}+6+\frac{-7}{6} \)(iv) \( \frac{-7}{4}+0+\frac{-9}{5}+\frac{19}{10}+\frac{11}{14} \)(v) \( \frac{-7}{4}+\frac{5}{3}+\frac{-1}{2}+\frac{-5}{6}+2 \)
- Out of the ratios $7: 20 ; 13: 25 ; 17: 30$ and $11: 15$, find the smallest one.
- Name the property of multiplication of rational numbers illustrated by the following statements:(i) \( \frac{-5}{16} \times \frac{8}{15}=\frac{8}{15} \times \frac{-5}{16} \)(ii) \( \frac{-17}{5} \times 9=9 \times \frac{-17}{5} \)(iii) \( \frac{7}{4} \times\left(\frac{-8}{3}+\frac{-13}{12}\right)=\frac{7}{4} \times \frac{-8}{3}+\frac{7}{4} \times \frac{-13}{12} \)(iv) \( \frac{-5}{9} \times\left(\frac{4}{15} \times \frac{-9}{8}\right)=\left(\frac{-5}{9} \times \frac{4}{15}\right) \times \frac{-9}{8} \)(v) \( \frac{13}{-17} \times 1=\frac{13}{-17}=1 \times \frac{13}{-17} \)(vi) \( \frac{-11}{16} \times \frac{16}{-11}=1 \)(vii) \( \frac{2}{13} \times 0=0=0 \times \frac{2}{13} \)(viii) \( \frac{-3}{2} \times \frac{5}{4}+\frac{-3}{2} \times \frac{-7}{6}=\frac{-3}{2} \times (\frac{5}{4}+\frac{-7}{6}) \)
Kickstart Your Career
Get certified by completing the course
Get Started