Observe the following pattern `1=1/2{1xx(1+1)},` `1+2=1/2{2xx(2+1)},` `1+2+3=1/2{3xx(3+1)},` `1+2+3+4=1/2{4xx(4+1)}` and find the values of each of the following : `1+2+3+4+5++50,` `31+32++50`

Observe the following pattern 1^2=1/6[1xx(1+1)xx(2xx1+1)] , 1^2+2^2=1/6[2xx(2+1)xx(2xx2+1)] , 1^2+2^2+3^2=1/6[3xx(3+1)xx(2xx3+1)], 1^2+2^2+3^2+4^2=1/6[4xx(4+1)xx(2xx4+1)], and find the values of each of the following 1^2+2^2+3^2+4^2+ddot+10^2, 5^2+6^2+7^2+8^2+9^2+10^2+11^2+12^2

3.Find the value of (5^0 +4^-1) times 2^2

Find the values of each of the following : (2^(-1)xx\ 4^(-1))-:2^2 (ii) (5^(-1)xx\ 2^(-1))-:6^(-1)

Observe the following pattern (1xx2)+(2xx3)=(2xx3xx4)/3, (1xx2)+(2xx3)+(3xx4)=(3xx4xx5)/3, (1xx2)+(2xx3)+(3xx4)+(4xx5)=(4xx5xx6)/3 and find the value of \ (1xx2)+(2xx3)+(3xx4)+(4xx5)+(5xx6)

Find the sum to n terms of the series : 1xx2xx3 + 2xx3xx4 + 3xx4xx5 + ...

Find the values of each of the following : (1/2)^(-1)+\ (1/3)^(-1)+\ (1/4)^(-1) (1/2)^(-2)+\ (1/3)^(-2)+(1/4)^(-2)

Find the value of each of the following: (i)((-1)/2)^2xx2^3xx(3/4)^2 (ii) ((-3)/5)^4xx(4/9)^4xx((-15)/(18))^2

Express the following as a rational number: (1/2)^3xx((-3)/5)^3xx((-4)/9)^2

Observe the following pattern 1+3=2^2 1+3+5=3^2 1+3+5+7=4^2 and write the value of 1+3+5+7+9+ upto n terms.

Find the sum of the following infinite series 1/2(1/5)^2+2/3(1/5)^3+3/4(1/5)^4+