series summation - JMO

Pages of a book are numbered from one onwards. A boy has torn one page of the book. If sum of page numbers of remaining pages of the book is 1620.
Then (1) find page number of torn page and
(2) How many pages the book had ?

JMO ---- STD V and VI

Answer:

sum of pages = n(n + 1)/2

we will check will 50, 55, 60, 65 as total number of pages

sum of pages = S

S(50) = 50 x 51/2 = 1275

S(55) = 55 x 56/2 =  1540

S(60) = 60 x 61/2 =  1830

Since the total sum of pages after a page us torn is 1620, the number of pages in the book will be in the range of 55 to 60

S(56) = 56 x 57/2 = 1596

S(57) = 57 x 58/2 = 1653

So, the book had 57 pages.

and 1653 - 1620 = 23

so, the 23rd page was torn off.