The sum can be written as
Good Day!
Please help me solve this problem!
Find the sum of
(1 - 1/6) + (1/2 - 1/7) + (1/3 - 1/8) + ....+ (1/995 -1/1000)
I guess it has something to do with arithmetic progression but I can't find their common difference. I guess my idea is wrong.
Thanks,
As given by red_dog, we calculate;
S = (1/1 - 1/6) + (1/2 - 1/7) + (1/3 - 1/8) + ....+ (1/995 -1/1,000)
S = 1/1 + 1/2 + 1/3 + 1/4 + 1/5 - 1/996 - 1/997 - 1/998 - 1/999 - 1/1,000
S = 1/1 + 1/2 + 1/3 + 1/4 + 1/50 - 1/996 - 1/997 - 1/998 - 1/999 - 1/1,000
S = 137/60 - 206671037501/41251456251000
S = 93984154068949/41251456251000
S = 2 + 11481241566949/41251456251000
S = 2 + 0.2783233032329780 . . . .
S = 2.2783233032329780 . . . .