The sum of n terms of m A.P.s are $$S1$$, $$S2$$, $$S3$$, …, Sm. If the first term and common difference are $$1$$, $$2$$, $$3$$, …, m respectively, then $$S1$$ $$+$$ $$S2$$ $$+$$ $$S3$$ $$+$$ … $$+$$ Sm $$=$$

Question

The sum of n terms of m A.P.s are $$S1$$, $$S2$$, $$S3$$, …, Sm. If  the first term and common difference are $$1$$, $$2$$, $$3$$, …, m  respectively, then $$S1$$ $$+$$ $$S2$$ $$+$$ $$S3$$ $$+$$ … $$+$$ Sm $$=$$

Infinity Learn · Accepted Answer

We have, $$S1=(n/2)$$[$$2$$⋅$$1+(n$$−$$1)$$⋅$$1$$]$$S2=(n/2)$$[$$2$$⋅$$2+(n$$−$$1)$$⋅$$2$$]$$Sm=(n/2)$$[$$2$$⋅$$m+(n$$−$$1)$$⋅m]∴$$S1+S2+$$…$$+Sm=n(1+2+3$$…$$+m)+n(n$$−$$1)2$$×(1+2+$$…$$+m)=m(m+1)2n+n2$$−$$n2=m(m+1)2$$⋅$$n(n+1)2=14mn(m+1)(n+1)

The sum of n terms of m A.P.s are S₁, S₂, S₃, …, S_m. If the first term and common difference are 1, 2, 3, …, m respectively, then S₁ + S₂ + S₃ + … + $S_{m}$ =

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The sum of n terms of m A.P.s are S1, S2, S3, …, Sm. If the first term and common difference are 1, 2, 3, …, m respectively, then S1 + S2 + S3 + … + Sm =

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The sum of n terms of m A.P.s are S₁, S₂, S₃, …, S_m. If the first term and common difference are 1, 2, 3, …, m respectively, then S₁ + S₂ + S₃ + … + $S_{m}$ =