Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

What is the sum of the first 50 natural numbers? How to solve it without adding 50 digits?

Sagot :

[tex]1+2+3+4+5+\dots+50\\\\1;\ 2;\ 3;\ 4;\ 5;\dots;50\ are\ the\ terms\ of\ a\ arithmetic\ sequence\\where\ a_1=1\ and\ d=1\\\\Sum:S_n=\frac{a_1+a_n}{2}\cdot n\\\\S_{50}=\frac{1+50}{2}\cdot50=51\cdot25=1275\leftarrow solution[/tex]
AL2006
Look at the first one and the last one:                  1 + 50 = 51
Look at the second one and the second-last one:  2 + 49 = 51
Look at the third one and the third-last one:           3 + 48 = 51

Every pair you construct in this way adds up to 51 .

There are ( 50/2 ) = 25 pairs.

They all add up to ( 25 pairs ) x ( 51 per pair ) = 1,275
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.