Q. 53.5( 6 Votes )

# Evaluate :</p

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    Rate this question :

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