1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + … to n terms Solution: Let the nth term of the given series be given by Tn. According to the question: $ {{T}_{n}}~=\text{ }n\left( n+1 \right)/2 $ $...
1.2.4 + 2.3.7 + 3.4.10 + … to n terms. Solution: Let the nth term of the series be given by Tn According to the question: $ {{T}_{n}}~=\text{ }n\text{ }\left( n\text{ }+\text{ }1 \right)\text{...
1.2.5 + 2.3.6 + 3.4.7 + …….. Solution: Let the nth term of the series here be given by Tn We know that: $ {{T}_{n}}~=\text{ }n\text{ }\left( n\text{ }+\text{ }1 \right)\text{ }\left( n\text{...
23 + 43 + 63 + 83 + ……… Solution: Let the nth term of the given series be given by Tn We have: Tn = (2n)3 = 8n3 Let the sum of n terms of the given series be represented by Sn We have: Therefore,...
13 + 33 + 53 + 73 + …….. Solution: Let the nth term of the series be given by Tn We have: $ {{T}_{n}}~=\text{ }{{\left[ 1\text{ }+\text{ }\left( n-1 \right)2 \right]}^{3}} $ $ =\text{ }{{\left( 2n-1...