[1+(1+3)+(1+3+5)+..." to "n" terms."],[1^(2)+(1^(2)+2^(2))+(1^(4)+2^(2)+3^(2))+..." to "n" term "]

(i) 1+(1+2)+(1+2+3)+………. to n terms. (ii) 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2))+ ………………to n terms.

1^(3) + 1^(2) + 1+2^(3) + 2^(2) + 2+3^(2) + 3^(2) + 3+3… 3n terms =

(1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1+ 2+ 3)+ …. + n terms =

1 + (1 +2) + (1 + 2 + 3) + …. To n term is

1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+.. . to n terms =

1+(1+2)+(1+2+3)+(1+2+3+4)+ to n terms.

The sum of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1^(2)+2^(2)+3^(2))+...... upto n terms,is

Find the sum of n-terms: [(1/1)+(1^3 +2^3)/2 +(1^3 +2^3 +3^3)/3+....to n -terms

underset(n to oo)lim ((1+2+....+"n terms")(1^(2)+2^(2)+...+"n terms"))/(n(1^(3)+2^(3)+...+"n terms"))=

STATEMENT-1 : If 1^(2) - 2^(n) + 3^(2) …….."to" 21 terms is 231 STATEMENT-2 : If 1^(3) - 2^(3) + 3^(3) - 4^(5) ……….. to 15 terms is 1856 STATEMENT-3 : If 1^(1) + 3^(2) + 5^(2) …….. to 8 terms is 689