3 + 7 + 14 + 24 + 37 + … Solution: Let Tn be the nth term and Sn be the sum to n terms of the given series. We have, Sn = 3 + 7 + 14 + 24 + 37 + …………. + Tn-1 + Tn … (1) Equation (1) can be rewritten...

1 + 3 + 7 + 13 + 21 + … Solution: Let Tn represent the nth term and let Sn represent the sum to n terms of the given series. According to the question: $ {{S}_{n}}~=\text{ }1\text{ }+\text{ }3\text{...

2 + 5 + 10 + 17 + 26 + ……….. Solution: Let Tn and Sn be the nth term and the sum of n terms respectively, of the given series. Then, we have: $ {{S}_{n}}~=\text{ }2\text{ }+\text{ }5\text{ }+\text{...

   3 + 5 + 9 + 15 + 23 + …………. Solution: Let Tn and Sn be nth term and the sum of n terms respectively, of the given series. Then, according to the question: $ {{S}_{n}}~=\text{ }3\text{...

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,...