Solve this

Asked by Sddmath2015 | 4th Sep, 2018, 11:24: PM

Expert Answer:

1 + (2 + 3) + (4 + 5 + 6) + ..... n terms
1 + 2 + 3 + 4 + 5 + 6 + ......n terms
Hence, total number of terms are begin mathsize 16px style fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction end style.
Sn = begin mathsize 16px style fraction numerator straight m open parentheses straight m plus 1 close parentheses over denominator 2 end fraction space where space straight m equals fraction numerator straight n open parentheses straight n plus 1 close parentheses over denominator 2 end fraction end style
Hence, we get begin mathsize 16px style fraction numerator begin display style fraction numerator straight n open parentheses straight n plus 1 close parentheses over denominator 2 end fraction open square brackets fraction numerator begin display style straight n open parentheses straight n plus 1 close parentheses end style over denominator begin display style 2 end style end fraction plus 1 close square brackets end style over denominator 2 end fraction equals 1 over 8 straight n open parentheses straight n plus 1 close parentheses open parentheses straight n squared plus straight n plus 2 close parentheses end style

Answered by Sneha shidid | 6th Sep, 2018, 12:46: PM

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