$1 + 3 + 5 + 7 + 9$+$\ldots upto 40 terms is equal to 2 2$
Step-by-Step Solution
Key Concept: Recognize$1+3+5+\cdots$as the sum of the first$40$odd numbers.
($1 + 5 + 9$+$\ldots$$\ldots upto 20 terms ) + ($3 + 7 + 11+...upto$20 terms) 2 2 2$(2)$20 2 20 =$$\sum($4r - 3)$+$$\sum($4r - 1)$$r=1$$r=1$20 2 =$$\sum($4r - 3) + (4r - 1)$$r=1$20 2 = 4$$$\sum ($$4r - 5r + 2)$$r=1$20 20 20$2 = 1$6$$\sum$r - 2$0$$$\sum r + 8$$$\sum$1 = 41880$$r=1$$$$r=1$r=1$
Correct Answer: 2