Q4 of 104 Page 457

Find the sum :
…. To 2n terms

We can split the above expression into 2 parts. We will split 2n terms into 2 parts also which will leave it as n terms and another n terms .

Sum of a G.P. series is represented by the formula, , when |r|<1. ‘S_n’ represents the sum of the G.P. series upto n^th terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.

Here,

a =

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

n terms

∴

⇒

∴

More from this chapter

All 104 →

2 E

Find the sum of the GP :

x(x + y) + x²(x² + y²) + x³(x³ + y³) + …. To n terms

Find the sum to n terms of the sequence :

(i) ,….. to n terms

(ii) (x + y), 9x² + xy + y²), (x³ + x2y + xy² + y³), …. to n terms

Evaluate :

NOTE:In an expression like this ⇒ , n represents the upper limit, 1 represents the lower limit , x is the variable expression which we are finding out the sum of and i represents the index of summarization.