[indiancomet]

Originally Posted by zango @ Tue Oct 05, 2004 3:35 pm

And can be derived as the sum of an Arithmetic progression:

b
Sn = Σn = (b - a + 1)(b+a)/2 = (sqr(b) - sqr(a) + b + a) /2
n = a

Where, the common difference d is 1.

It helps to remember the formulae for sum of terms (AP/GP/HP/Squares/Natural numbers/Cubest) etc, coz all other things can be derived therefrom.

Cheers!

Hi Guys,
Can someone tell me the furmula for the sum of an HP series. I can't recall studying one...maybe there is a approximate formula...
Thanks guys..

[Debs]

HP of a and b = 2* a* b / (a+b)

[Asif]

HP of a and b = 2* a* b / (a+b)

hey deb i dont agree wid u..

(i) Theres no general formula for the sum of any number fo terms in HP.questions based on HP are generally solved by converting them into a AP by taking reciprocal of the terms.

(ii) The HP of a and b is (2*a*b)/a+b.

---AsIf

[Debs]

hi,
i agree with u that for HP, we need to convert them to AP first. For 2 numbers, the formulae is correct. However, for 3 or 4 terms we need to derive it by taking reciprocals.
So better to stick to basics.
Debs

[Asif]

thnx for the sincere agreement debs
---AsIf

[singh782000]

Can someone give me a detailed methodology for solving questions pertaining to the following variety?
-> Find the number of numbers between 300 and 400 (both included) which are divisible by 2,3,4,5 and 7?
Detailed analysis is required, 'cause these problems are quite common in CAT these days.

[Syberite]

Hey guys !

gr8 thread man! keep it up.

Well I would like to add one more trick to the discussion. This one is from vedic maths.

I f you want to calculate square of a two digit number ending in 5 for ex.45, 55,65 etc.
The method is as follows. for ex. if you want to calculate 45*45 then write down 25 as the last two digits of the product. then multiply 4 with 5=20 and write down as first two digits of the product. therefore 45*45=2025. similarly 55*55= 3025.

Funda is, write 25= square of 5 as last two digits of the product and multiply the digit in ten's place of the original no. by its immediate higher digit and write this no as first two digits of the product.

25*25= (2*3=6)25=625,
95*95=(9*10=90)25=9025.

Cheers!

Syberite.

[Debs]

hi,
in such cases, we need to apply Set funda.
at times it really becomes a bit difficult because of common terms like a number having factor of 2, 3, 5.........
In ur case, we need to look for number which are factors of 2, 3, 5, 7.
Terms with factor of 2 b/w 300 and 400 (both being inclusive): 200 - 149 = 51
Terms with factor of 3 b/w 300 and 400 (both being inclusive): 133 - 99 = 34
Terms with factor of 5 b/w 300 and 400 (both being inclusive): 80 - 59 = 21
Terms with factor of 7 b/w 300 and 400 (both being inclusive): 57 - 42 = 15
Terms with factor of 6 (LCM of 2 and 3) b/w 300 and 400 (both being inclusive):
Terms with factor of 14 b/w 300 and 400 (both being inclusive):
Terms with factor of 10 b/w 300 and 400 (both being inclusive):
.........
like that u need to continue........
If there is any other shortcut, do let me know...
Debs

[fruskee]

Debs & singh782000,
An easier method would be to find the LCM of (2,3,4,5,7).
And look for the number of multiples of this LCM in the range 300 to 400.

[Debs]

ohh yes, i missed the keyword "and" in between. i took it as "or". :( u r right, we need to take LCM only.
Debs.