Question

Find a formula for Sum of the first n terms of the series-
a) √3 + 3 + 3√3 +9....
b) 0.9 + 0.09 + 0.009....

Answer 1

familiar with the formula of sum of infinite terms in an Geometric sequence??

Answer 2

i dont think it goes to infinty!

Answer 3

infinity*

Answer 4

oops, n terms.....so ther's a formula for sum of 'n' terms of GP,familiar with that ? @amishra

Answer 5

Yes, I got the formula, but I didn't get the answer

Answer 6

whats your r in both case.....common ratio??

Answer 7

For the first one, it's √3, and for the second, its 0.1.

Answer 8

correct...so after substituting in that formula , u get
\[\frac{\sqrt{3}(-1+(\sqrt{3})^n)}{(-1+\sqrt{3})}\]
and \[\frac{0.1(1-(0.1)^n)}{0.9}\]
are these the answers u get or the given answers?

Answer 9

Yes, I got these answers, but the given answers are more simplified :/

Answer 10

like ? can u show them....then i'll try to simplify

Answer 11

a) (3+√3) * ((√3)^n -1) / 2
b) 1- (0.1)^n

Answer 12

in the 2nd equation,the numerator should have 0.9 instead of 0.1(as 1st term=0.9)
so the 2nd equation directly simplifies to 1-(0.1)^n.....because 0.9 cancels in numerator and denominator

Answer 13

Oh, yeah, I got that, what about the first one?

Answer 14

for 1st they have rationalized the denominator by multiplying (1+root 3) in numerator and denominator.....so denominator became (3-1)=2...got it?

Answer 15

Oh! I got it now! Wow! Thank you so much, again!!! :D I would have died if you weren't there! :D Thank you!