Answer :

We can write this as (2 + 31)+(2+32) + (2 +33)+… to 10 terms


= ( 2+2+2+… to 10 terms) + ( 3+32+33+… to 10 terms)


= 2×10 + (3+32+33+… to 10 terms)


= 20 + (3+32+33+… to 10 terms)


Sum of a G.P. series is represented by the formula, , when r≠1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.


Here,


a = 3


r =(ratio between the n term and n-1 term) 3


n = 10 terms






Thus, sum of the given expression is


= 20 + (3+32+33+… to 10 terms)


= 20 + 88572


=88592


(ii) The given expression can be written as,


( 21 + 31-1) + (22 + 32-1) + …to n terms


= (2 + 30) + ( 22+ 31) + …to n terms


= (2 + 1) +(22 + 3 ) + …to n terms


= (2 + 22 + …to terms) + ( 1 + 3 + … to terms)


Sum of a G.P. series is represented by the formula, , when r≠1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.


Here,


a = 2, 1


r = (ratio between the n term and n-1 term)2, 3


terms





(iii) We can rewrite the given expression as


( 51 + 52 + 53+ …to 8 terms)


Sum of a G.P. series is represented by the formula, , when r>1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.


Here,


a = 5


r =(ratio between the n term and n-1 term) 5


n = 8 terms






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